Alright I guess I'll give some good input.
Phase 1:
[collapse="Phase 1 Map"]
The numbers refer to positions on stage.
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At the starting position, you end up on either one or two. If you are one platform one, I suggest either doing a simple drop through or run off platform PKFire. If you are one platform two, then you can choose from several options, but run off PKFire doesn't work very well due to the stage geography.
The main goal of this phase is to prevent your opponent setting up camp in section three. It has several natural barriers of protections that make is extremely hard to approach. Characters such at Snake, ROB, Link and Toon Link can make very good use of that section.
So, what to do about it? First, you don't let them take it, set up your own camp in there. Only Snake should be your real problem when dealing with camping down below, since his grenades roll down section four. Be prepared for a weakly charged gyro or laser from ROB. It shouldn't be too hard to shield the gyro after PSI Magnet because it goes much slower since it isn't fully charged. Against Link and Toon Link, you have to worry about most of his projectile spam since that all basically can go down. If you happen to shield an uncooked bomb, and he isn't approaching, then you can try to pick it up. But that doesn't do much good since it doesn't throw upward.
So what do you do if they've captured section 3? Well, approaching them will be a pain in the ***. I really don't recommend that. Instead, platform camping on section two would be advisable. Most of their projectiles can't hit a platform camper very well and Lucas has above average air mobility. You also have to remember that the stage eventually changes, so you will have a chance to get some damage on them.
Some other tips: When you are on section 4, grabbing is not advisable, Lucas grab goes with the slope, so it's range isn't where it should be and Lucas will have a hard timing actually landing the grab.
D-smashing while standing on Section 5 onto section 4 exposes even more of the hitbox of Lucas' d-smash making it harder to approach from section 3.