You're Falco. He's not.
Seriously though, a few ideas to (possibly) help:
If it's the PK Freeze giving you trouble, shine is a reflector, and I think they have yet to fix the glitch where you can jump out of shine immediately after it's reflected something, so PK Freeze shouldn't pose problems, given its moderate startup lag, unless you're just starting a laser (you can reflect them and jump or wavedash out of shine). Technically he can absorb your lasers but I think they heal him like 7% tops so at low percents that's just one hit of a combo (every percent does matter but forcing him to down+B or shield might be useful as a bait so it doesn't mean forget the lasers - also not all Lucas players will absorb it).
His zair recovery has deceptively long range - get on the edge early (if you knocked him far enough away that he can't down+B and jump back on), and if he PK Thunders you have enough time to drop and refresh invincibility. If he zairs to recover, you should be able to wait until he pulls himself up then quickly jump up [drop off jump] (because you've been sitting there so no lag) and punish with nair, dair, or fair and go from there [his animation is fixed for several frames [he can't do anything for a bit] when he pulls himself up while someone's on the ledge so his tether is punishable - pretty sure players like PP and M2K punish zair recoveries frequently in this game, because they've practiced it a lot].
If there's other specific stuff giving you trouble, be more specific as to what he's doing/the issue you're having.