Here's my take on some of the matchups (I've recently picked up Lucas in Brawl and Smash 4 so I'm not a complete expert on the matter).
1. Lucas vs. Pikachu, this match up is largely in Pikachu's favor due to his speed. If the Lucas player is able to predict what their opponent will do, it's easier to lead into PK Fire, or a grab, and (if you're opponent is extremely predictable) up-smash. The key is to pace the match, figure out what your opponent's strategy is, and do your best to adapt. Leave the smash moves for definite KOs, largely due to their end lag. If they miss Pikachu, he can easily lead into combos or a KO.
2. Lucas vs. Cloud, this match up is moderately in Cloud's favor. As noted by several other posters, due to his usage of limit. It is true that you'd have to chase down Cloud to make certain moves or place himself at a certain position on the field. Cloud isn't a large threat on a field like Final Destination because it's linear and he'd be forced to dodge your PK Fire, grabs, and zair (snake rope). If he attempts Blade Beam, you can easily absorb that and heal yourself (somewhere around 4%). I've found that chasing Cloud down w/ PK Thunder is decent in stopping him from charging his limit. However, it can leave you vulnerable if it doesn't land.
3. Lucas vs. Ness, a battle for the ages. Slightly to Ness' advantage, since his moves don't have as much lag as Lucas's do. It really boils down to getting close to Ness and maintaining pressure for the entire round (remember, Ness has the Behemoth Back Throw. So don't get sloppy). A battle of PK Fire will become old and predictable, eventually one or both of you will use PSI magnet, so properly timing your usage of PK Fire is essential.
4. Lucas vs. Bayonetta, arguable in Bayo's favor. The thing to keep in mind is that Bayonetta's move have a lot of end lag. You're better off spacing her w/ PK Fire or waiting for her to attack, shield/avoid it, and lead into a grab combo (you can also rotate from grabs to a few moderate jabs/PK fire.
5. Lucas vs. Ike, either even or in favor of Lucas. Reasoning: Ike is a slower character, as long as you don't let him pressure you, Lucas can stop half of his moves w/ PK fire, follow up w grabs (do so wisely), and easily pace/space the match until it's time to go for the KO. Ike, like most heavier characters, deals a lot of damage w/ very few hits. The key is to avoid them as much as possible, and punish them when they miss.
6. Lucas vs. Link/Toon Link, literally one of the hardest matchups for me. Lucas can't absorb anything (maybe their bombs, I've never tried it) and if he's too busy absorbing something they can easily follow w/ an arrow or boomerang. It's hard to close on on these two due to their swords and grabs. However, a missed grab is an opportunity given, so take advantage of those. Again, PK fire is very useful in giving yourself distance while accumulating damage. Your best bet, is to either space them out or force them to approach (don't let your opponent approach if you're not planning on punishing it).
General Rules for any matchup:
1. Determine if you have to play defensively (spacing) or offensively (grabs, jabs, smash attacks) and when to alternate between the two.
2. DO NOT SPAM PK THUNDER. It's very annoying and predictable (especially in for glory). And if you're opponent is faster, you'll get punished for it every time.
3. Look at this list for things that can be absorbed w/ PSI Magnet
http://www.ssbwiki.com/Absorption I'm not sure if they all can be absorbed by PSI Magnet.
4. Your bat is your friend. Although it may not be the best thing to use close range, it can deflect almost any projectile. However, the projectile changes in it's angle.
5. PK Fire & Zair are great spacing/approaching tools when used wisely.
6. Timing and adapting to your opponent is key. Especially when they're faster or hit harder.
7. PK Thunder and PK Freeze are great edge guarding tools. Depending on the recovery, PK thunder is a great method for gimping your opponent. PK Freeze, will often force opponents to air dodge or attempt to recover sooner than they should.
If there's anything I missed, I'll attempt to address it later.