One of the biggest issues Lucas has in a lot of his matchups is that he has very limited approaches. Far too many Lucas players try to get by on just SH Nairs to approach their opponents which is insufficient for many reasons which I will go into more detail later. To deal with Lucas's limitations, I believe it is necesary to develope a library of different approaches in order to maintain unpredictability and vary your approaches depending on the behaviour of your opponent and their characters' strengths and weaknesses. This is a short compilation of the most viable approaches for Lucas and their respective strengths and weaknesses.
Ground Approaches
Shield Cancel Jab
Basic enough. Just run toward your opponent, shield when you are the proper distance, put the shield down and start jabbing.
Strengths: High priority. Can shield projectiles or enemy attacks in process. Third hit has decent knockback. Good against spotdodgers.
Weaknesses: Lag while shield is dropping. Can be very predictable. Punished by shieldgrabs or attacks out of shield.
Shield Cancel Ftilt
See above only use a Ftilt. Spacing should be further from opponent than above.
Strengths: High priority. Can shield projectiles or enemy attacks in process. Good knockback with sweetspot. With IASA and proper spacing is near impossible to be punished unless opponent perfect shields or spotdodges.
Weaknesses: Punished by spotdodgers.
Pivot Grab
Run behind the opponent and quickly press toward them and Z to grab with reduced lag if it misses.
Strengths: Less lag than regular shield grab. Punishes shieldspammers. Good knockback and damage. Can lead to easy edgeguarding. Mindgame.
Weaknesses: Still laggy enough for serious punishment if misses. Punished by opponents reacting to your approach and attacking before you get behind them. Punished by spotdodgers and rollers.
Spotdodge Slide
Inspired by M2K's Fox in Melee. Run toward the opponent and as you get close, spotdodge while running retaining your momentum and sliding invincibly through your opponent. Fsmash behind you to hit opponent.
Strengths: Great mindgame. High knockback and damage. Punishes spotdodgers and opponents attacking to prevent your approach.
Weaknesses: Punished by perfect shield, shield and rolls. Laggy if prevented.
Aerial Approaches
SHFF Nair (combo)
Short hop, Nair immediately and fast fall, avoiding the final knockback hit (autocancel not necesary.) Combos into Utilt, Ftilt, Jabs, SH Uair reliably. Some others with luck.
Strengths: High damage. Punishes shields, spotdodge, and rolls.
Weaknesses: Low priority. Punished by most enemy attacks. If shielded all the way through can be punished after the combo. Perfect shielding on initial hit of Nair stops it. Gets predictable fast.
SHFF Nair (knockback)
Short hop, Nair immediately and fast fall so that it autocancels and hits opponent with the final knockback hit. Chase with PK Fire, Fairs or Nairs.
Strengths: Knockback varies little from percentage. Leads to easy edgeguarding. Punishes shield, spotdodge, and rolls. Unlike above, if shielded all the way through can be repeated for shield pressure.
Weaknesses: Low priority. Punished by most enemy attacks. Perfect shielding on initial hit stops it. Gets predictable fast.
FHFF Nair
Full hop, Nair at the peak of your jump and fast fall so that the final hit occurs as you touch the ground and autocancel. Chase with PK Fire, Fairs or Nairs.
Strengths: Knockback varies little from percentage. Leads to easy edgeguarding. Punishes shield, perfect shield, spotdodge and rolls. If shielded can be followed by SHFF Nair for shield pressure. Mindgame.
Weaknesses: Low priority. Punished by most enemy attacks. Vulnerable to projectiles.
FHFF Dair
Full hop, Dair, fast fall so that the third and fourth or just the fourth hit of Dair connect and autocancel. Timing will depend on spacing and height of character. Around 90% (character dependent) leads into Fsmash, Fair or Dsmash (depending on if just hit 4 connects or if 3 and 4 connect.) Under around 90% leads into SHFF Nair, SHFF Uair, jabs, Ftilt or FHFF Dair.
Strengths: High damage and knockback combos. Punishes shield, perfect shield, spotdodgers, rolls and most attacks. Easy to control spacing.
Weaknesses: Susceptible during beginning full hop. Some attacks hit through (ex. Snake's Utilt.) Harder to pull off against shorter characters especially with good projectiles.
Double Jump FF Dair
Double jump, Dair and fast fall to hit with third and fourth or just fourth hits connect and autocancel. Combos same as above.
Strengths: Long distance. High damage and knockback combos. Punishes shield, perfect shield, spotdodgers, rolls and most attacks. Easy to control spacing. Does better against projectiles than above.
Weaknesses: More predictable. Susceptible during beggining of double jumps. Some attacks hit through (ex. Snake's Utilt.)
FH Fair
Full hop and immediately Fair while near opponents.
Strengths: Cannot be punished with proper spacing. Moderate knockback.
Weaknesses: Only works on tall and mid height characters. Can become predictable.
SHFF Uair (immediate)
RAR Short hop, immediately Uair and fast fall for autocancel. Repeat.
Strengths: Massive **** against big characters for juggling after the first hit. Lots of damage racked up. Weird hitbox. High priority.
Weaknesses: Punished by spotdodgers, shield, perfect shield and rolls. Predictable.
SHFF Uair (delayed)
RAR short hop, fast fall, Uair very near to ground for autocancel. Immediately SHFF Uair or SHFF Nair.
Strengths: Weird hitbox. High priority. Mindgame. Punishes shields and spotdodgers.
Weaknesses: Punished by perfect shield and rolls. Susceptible during airtime before nearing ground.
Projectile Approaches
PK Freeze
Neutral B. Never go the full distance to avoid punishment. Keep it close. Combos into PK Freeze, Usmash, Dair or PKT2.
Strengths: High damage combos. Massive hitbox. Mindgame. Low lag on end.
Weaknesses: Punished by shield (without proper spacing), perfect shield, roll, spotdodgers, airdodge and attacks. Rarely connects against good players.
PKT1
Up B. Loop around opponents' shields to avoid it getting eaten.
Strengths: Punishes shield, spotdodgers, airdodge, and rolls. Mindgame. Decent knockback and damage.
Weaknesses: High lag if missed. Punished by perfect shield.
PKT2 (standard)
Up B mindgames into PKT2 into opponent: loops, offscreen, false edgeguard etc.
Strengths: High damage and knockback. Mindgame.
Weaknesses: Punished by shield, spotdodgers, rolls, some attacks, good spacing. Difficult to pull off against experienced players. Danger of SD.
PKT2 (Thunderslide)
Up B approaching edges of platforms for faster PKT2 into opponents or for PK thunder cancel. Thunder cancel leads into any aerial on Battlefield or PK Fire.
Strengths: High damage and knockback. Mindgame. Faster than above. Better chance of hitting than above especially against players inexperienced at fight Lucas.
Weaknesses: Punished by shield, spotdodgers, rolls, and good spacing.
PK Fire (ground)
Forward B. Tilt rather than smash to avoid tripping.
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.)
Weaknesses: Punished by shield and perfect shield. Predictable.
SH PK Fire
Short hop and use PK Fire while approaching the ground for least possible lag closest to the ground. Follow up with jabs if opponent approaches (dependent on spacing.)
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.) Less lag than above.
Weaknesses: Punished by shield and perfect shield. More predictable than above.
Platform Fall PK Fire
Run off the side of a platform and use PK Fire while falling.
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.) Least predictable PK Fire approach.
Weaknesses: Punished by shield and perfect shield.
FH PK Fire (double jump)
Full hop and immediately PK Fire. Most useful against falling characters or characters on platforms. With proper timing you should be able to double jump before touching the ground. This is a great opportunity to PK Fire again or use a Fair.
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.) Double jump can be hard to predict. Mindgame.
Weaknesses: Somewhat technically difficult but if done correctly and used with proper spacing should be basically unpunishable.
Seems like a lot of good approaches right? WRONG!! Almost all of these are situational and will depend upon how your opponent is reacting and what character he is playing. This is why you need to be able to use ALL OF THEM. You'll notice I use the word "approach" pretty loosely. I mean any way that you can get damage in on an opponent without them coming to you first. If you have any suggestions on approaches or information to add feel free to post them.
Ground Approaches
Shield Cancel Jab
Basic enough. Just run toward your opponent, shield when you are the proper distance, put the shield down and start jabbing.
Strengths: High priority. Can shield projectiles or enemy attacks in process. Third hit has decent knockback. Good against spotdodgers.
Weaknesses: Lag while shield is dropping. Can be very predictable. Punished by shieldgrabs or attacks out of shield.
Shield Cancel Ftilt
See above only use a Ftilt. Spacing should be further from opponent than above.
Strengths: High priority. Can shield projectiles or enemy attacks in process. Good knockback with sweetspot. With IASA and proper spacing is near impossible to be punished unless opponent perfect shields or spotdodges.
Weaknesses: Punished by spotdodgers.
Pivot Grab
Run behind the opponent and quickly press toward them and Z to grab with reduced lag if it misses.
Strengths: Less lag than regular shield grab. Punishes shieldspammers. Good knockback and damage. Can lead to easy edgeguarding. Mindgame.
Weaknesses: Still laggy enough for serious punishment if misses. Punished by opponents reacting to your approach and attacking before you get behind them. Punished by spotdodgers and rollers.
Spotdodge Slide
Inspired by M2K's Fox in Melee. Run toward the opponent and as you get close, spotdodge while running retaining your momentum and sliding invincibly through your opponent. Fsmash behind you to hit opponent.
Strengths: Great mindgame. High knockback and damage. Punishes spotdodgers and opponents attacking to prevent your approach.
Weaknesses: Punished by perfect shield, shield and rolls. Laggy if prevented.
Aerial Approaches
SHFF Nair (combo)
Short hop, Nair immediately and fast fall, avoiding the final knockback hit (autocancel not necesary.) Combos into Utilt, Ftilt, Jabs, SH Uair reliably. Some others with luck.
Strengths: High damage. Punishes shields, spotdodge, and rolls.
Weaknesses: Low priority. Punished by most enemy attacks. If shielded all the way through can be punished after the combo. Perfect shielding on initial hit of Nair stops it. Gets predictable fast.
SHFF Nair (knockback)
Short hop, Nair immediately and fast fall so that it autocancels and hits opponent with the final knockback hit. Chase with PK Fire, Fairs or Nairs.
Strengths: Knockback varies little from percentage. Leads to easy edgeguarding. Punishes shield, spotdodge, and rolls. Unlike above, if shielded all the way through can be repeated for shield pressure.
Weaknesses: Low priority. Punished by most enemy attacks. Perfect shielding on initial hit stops it. Gets predictable fast.
FHFF Nair
Full hop, Nair at the peak of your jump and fast fall so that the final hit occurs as you touch the ground and autocancel. Chase with PK Fire, Fairs or Nairs.
Strengths: Knockback varies little from percentage. Leads to easy edgeguarding. Punishes shield, perfect shield, spotdodge and rolls. If shielded can be followed by SHFF Nair for shield pressure. Mindgame.
Weaknesses: Low priority. Punished by most enemy attacks. Vulnerable to projectiles.
FHFF Dair
Full hop, Dair, fast fall so that the third and fourth or just the fourth hit of Dair connect and autocancel. Timing will depend on spacing and height of character. Around 90% (character dependent) leads into Fsmash, Fair or Dsmash (depending on if just hit 4 connects or if 3 and 4 connect.) Under around 90% leads into SHFF Nair, SHFF Uair, jabs, Ftilt or FHFF Dair.
Strengths: High damage and knockback combos. Punishes shield, perfect shield, spotdodgers, rolls and most attacks. Easy to control spacing.
Weaknesses: Susceptible during beginning full hop. Some attacks hit through (ex. Snake's Utilt.) Harder to pull off against shorter characters especially with good projectiles.
Double Jump FF Dair
Double jump, Dair and fast fall to hit with third and fourth or just fourth hits connect and autocancel. Combos same as above.
Strengths: Long distance. High damage and knockback combos. Punishes shield, perfect shield, spotdodgers, rolls and most attacks. Easy to control spacing. Does better against projectiles than above.
Weaknesses: More predictable. Susceptible during beggining of double jumps. Some attacks hit through (ex. Snake's Utilt.)
FH Fair
Full hop and immediately Fair while near opponents.
Strengths: Cannot be punished with proper spacing. Moderate knockback.
Weaknesses: Only works on tall and mid height characters. Can become predictable.
SHFF Uair (immediate)
RAR Short hop, immediately Uair and fast fall for autocancel. Repeat.
Strengths: Massive **** against big characters for juggling after the first hit. Lots of damage racked up. Weird hitbox. High priority.
Weaknesses: Punished by spotdodgers, shield, perfect shield and rolls. Predictable.
SHFF Uair (delayed)
RAR short hop, fast fall, Uair very near to ground for autocancel. Immediately SHFF Uair or SHFF Nair.
Strengths: Weird hitbox. High priority. Mindgame. Punishes shields and spotdodgers.
Weaknesses: Punished by perfect shield and rolls. Susceptible during airtime before nearing ground.
Projectile Approaches
PK Freeze
Neutral B. Never go the full distance to avoid punishment. Keep it close. Combos into PK Freeze, Usmash, Dair or PKT2.
Strengths: High damage combos. Massive hitbox. Mindgame. Low lag on end.
Weaknesses: Punished by shield (without proper spacing), perfect shield, roll, spotdodgers, airdodge and attacks. Rarely connects against good players.
PKT1
Up B. Loop around opponents' shields to avoid it getting eaten.
Strengths: Punishes shield, spotdodgers, airdodge, and rolls. Mindgame. Decent knockback and damage.
Weaknesses: High lag if missed. Punished by perfect shield.
PKT2 (standard)
Up B mindgames into PKT2 into opponent: loops, offscreen, false edgeguard etc.
Strengths: High damage and knockback. Mindgame.
Weaknesses: Punished by shield, spotdodgers, rolls, some attacks, good spacing. Difficult to pull off against experienced players. Danger of SD.
PKT2 (Thunderslide)
Up B approaching edges of platforms for faster PKT2 into opponents or for PK thunder cancel. Thunder cancel leads into any aerial on Battlefield or PK Fire.
Strengths: High damage and knockback. Mindgame. Faster than above. Better chance of hitting than above especially against players inexperienced at fight Lucas.
Weaknesses: Punished by shield, spotdodgers, rolls, and good spacing.
PK Fire (ground)
Forward B. Tilt rather than smash to avoid tripping.
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.)
Weaknesses: Punished by shield and perfect shield. Predictable.
SH PK Fire
Short hop and use PK Fire while approaching the ground for least possible lag closest to the ground. Follow up with jabs if opponent approaches (dependent on spacing.)
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.) Less lag than above.
Weaknesses: Punished by shield and perfect shield. More predictable than above.
Platform Fall PK Fire
Run off the side of a platform and use PK Fire while falling.
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.) Least predictable PK Fire approach.
Weaknesses: Punished by shield and perfect shield.
FH PK Fire (double jump)
Full hop and immediately PK Fire. Most useful against falling characters or characters on platforms. With proper timing you should be able to double jump before touching the ground. This is a great opportunity to PK Fire again or use a Fair.
Strengths: Good damage. Punishes attacks, spotdodgers and rollers (dependent on spacing.) Double jump can be hard to predict. Mindgame.
Weaknesses: Somewhat technically difficult but if done correctly and used with proper spacing should be basically unpunishable.
Seems like a lot of good approaches right? WRONG!! Almost all of these are situational and will depend upon how your opponent is reacting and what character he is playing. This is why you need to be able to use ALL OF THEM. You'll notice I use the word "approach" pretty loosely. I mean any way that you can get damage in on an opponent without them coming to you first. If you have any suggestions on approaches or information to add feel free to post them.