FINALLY!!!
Well, There are two things I want to point out:
The more damage Lucario takes, the more powerful he becomes. Characters that can KO early can avoid this problem. Squirtle WILL have problems.
Lucario is somewhat light when it comes to vertical knockback, and the best way all three Pokemon KO is ^.
Lucario is My second, yet since I've been playing PT so much, Me playing him is rare. Despite this, I have been one of the people lurking around the Lucario Boards...
Lucario vs Squirtle: This is clearly a Lucario shutout (if there is one). for starters, Squirtle can't Kill Lucario Early, so Squirtle WILL feel the power of the Aura (and so many Dragon Ball Z memes). To compound this, Squirtle is Light, so a powered up Lucario is going to Hurt badly.
Please Ignore unless some other PT gives Confirmation
Lucario vs Ivysaur: Again, this goes to Lucario, yet it isn't much of a shutout as Squirtle. For starters, Ivysaur's Usmash (if it ever connects [it unlikely will]) and Uair (beware) will Both KO you upwards at around 70% or so, which doesn't really allow Aura to kick in as much. Conversely, Low power Lucario will likely gimp you, and Ivysaur is a prime candidate for "worst recovery in Brawl". If Ivysaur ever leaves the stage, Game over.
Please Ignore this until some other PT gives confirmation (I am not an expert on Squirtle or Ivysaur)
Lucario vs Charizard:
For Charizard: For starters, Charizard is really powerful, and strong. He is very capable of KOing Lucario at around 70%. Charizard himself is quite heavy, so Trying to KO him is a problem. This is also a problem because Charizard has a good recovery (around or a bit better than Lucario's for perspective). Compound this with super armor fly, and Gimping would be nightmarish. Charizard's U attacks can easily juggle Lucario, and Lucario's obvious Dair may be his only hope. If Charizard sees it coming, expect a shielded Usmash (requires that tap jump is on). He has several moves to Kill you, even horizontally (All tilts, usmash, rock smash, fair, bair, dair [on occasion], rock smash, and rarely, Fsmash and Dsmash). Let's not forget the grab game, as Charizard can throw you around a lot.
Against Charizard: Starting with His grab, Lucario abnormally lacks some friction, so he can't be regrabbed. Secondly, Aura sphere is a decent Projectile, and Charizard has NO defense against Projectiles. Also, Lucario himself, is a good Juggler, which is just as bad against Charizard as around half of the list for him is against you. Charizard has less defense against Juggling than Lucario (Nair may be the only real attack that works). Lucario could theoretically just Juggle Charizard into a comfortable range to KO him, and do so. This is even worse if Charizard decides to spare you. Let's not forget the air game, Lucario can use that to hurt you. Oh, and since this isn't pokemon, Charizard can't suck up your fighting moves and counter it with fire ones.
Confirmation preferred, but you CAN listen to this beforehand.
Really, Lucario has a complete upper hand against Squirtle, one against Ivysaur, and a slight one against Charizard (or even, it depends on which Pros and cons are more severe)