The most important thing is to play Lucas like Lucas. Constantly mix up your approach options, or just don't approach and throw a safe move out like retreating zair/fair/PK fire, FH dair, etc. I also find mixing up fullhop aerials with shorthop ones helps, especially given how mobile Lucas is in the air. It'll make opponents really question what you're opting for -- a read/mixup or fade/fakeout.
Some things I find helpful in a pinch is RAR nair to cross up their shield if they expect something like normal nair and don't react out of shield well. One of Lucas' biggest problems is dealing with getting read and shieldgrabbed on a misspaced aerial. RAR nair puts you behind their shield, and not many characters can punish Lucas from that position, nor will many players be prepared for it.
Once you get your opponent in a disadvantageous position, do not stop going aggro on them until you're reset to neutral or they die, but also keep playing very unexpectedly. Throw in a well-spaced b-reversed magnet or go for a roll read > grab. Or read a sidestep and opt for nair/dsmash, or read a jump and chase with uair/dair/fair depending on the situation. Lots of opponents just crumble when you lower their defensive options via reads and option coverage with Lucas' great mixup tools.
Also, when in doubt in super-close quarters, remember that jab is frame 2 with a FAF of only 20 frames on both jab 1 and 2. This means if you mess up spacing on say, fair, you can FF it and buf jab 1, and depending on whether your opponent drops shield or not, read their reactions to get yourself in a better position. For example, if they stay in shield and you connect with jab 1, you can either do jab 1 > retreat or Jab 1 > shield pressure options, e.g. crossup nair, dair, grab (though the latter is fairly unsafe and slow of course), OR jab 1 > jab 2 > cancel into any of the options I listed a moment ago. Granted, compared to many OOS options, this is fairly unsafe frame wise, but Lucas isn't exactly a frame data god. We gotta work with our mixup tools.
Another thing to remember is that zair eats certain projectiles. I'm fairly certain it eats Luigi's fireball, don't know about Ryu's projectiles, and I think it also eats weaker Mewtwo shadow ball? Also, I think fair can do this, though it's not recommended unless you're dropping down right on top of/in front of a Luigi doing fireball and want to both intercept the fireball and also hit Luigi.