My opinion (HUZZAH!):
I've played with a guy who uses Pokemon Trainer, albeit only for low tier stuff, but he's still quite good.
Charizard: IMO, Lucas ***** Charizard. He is huge, and is a massive target for nair. He is also quite slow, and gets hit with so many of Lucas' moves. Lucas relatively beats Charizard off stage, just watch for the spike. I don't see Charizard being too much of a problem for Lucas. He's kinda like Bowser, except he can fly. Kinda. I say 65/35 in Lucas' favor.
Ivysaur: Despite what the guy has said before, I really don't see Ivysaur being too much of a problem for Lucas. Granted, razor leaf does outrange PK fire, and is a decent projectile, but other than that, I don't see much going for Ivysaur. Except for bullet seed, although it can be DI'd out of quickly if not directly hit into it. Offstage, I don't see Ivysaur as being able to do ANYTHING. And gimping him? Too easy. Rope Snake/ledge hugging **** Ivysaur too much. I'd probably put this one as 65/35 in Lucas' favor as well.
Squirtle: In my opinion, the best of the three pokemon. Squirtle is fast, and has an air game that is better than Lucas'. A well played Squirtle can do some sick stuff in this matchup. I also think Squirtle has a grab release chain grab on Lucas? But then again, who doesn't? I put this one as definitely lower, but I think this is still probably in Lucas' favor, but barely. I say 55-45 or so.
That's what I think, and I'm pretty sure I'm somewhat correct. Pokemon Trainer isn't that good.