I'm not a big fan of Ivysaur vs Lucario.
Lucario is much faster than Ivysaur, has a down B that lets him threaten a larger space in front of him than Ivy can, and has a projectile that Ivy can't kill quickly and reliably with jab, tilt, aerials, or specials. Not only that, but Lucario's aggression is much safer on Ivysaur (whos out of shield options are limited) than the average character. On the other side of that coin, Ivysaur's close range pressure isn't exactly air-tight to begin with. These things combined make neutral very unpleasant for Ivysaur. The neutral game mostly involves Ivy feeling cornered a lot, throwing out a lot of anticipatory moves to try and stay safe, and trying to trick him into wasting his aura charges, so it's easier to throw him offstage and gimp him.
Gimping with bair is the biggest thing Ivy has going for her in the match-up, especially if you're familiar with the Lucario you're fighting, and how they recover. Lucario can't easily gimp Ivysaur, so he mostly plays the standard "hold ledge and punish reel in" game against recovering Ivysaurs. That's not as good as Ivy's options on him, but it's decent.
They've both got pretty decent combo games on eachother, and both kill off the top pretty well with uairs and Up B shenanigans. However, since Ivy has killing off the sides and bottom (through edge-guarding) over Lucario, it's a good decision for her to ban low ceilings and put more emphasis on that advantage, trying to take him to stages with large offstage areas. Because of Lucario's neutral advantage, he'd probably want to take Ivy to a stage with a small main platform, where there's less leg room for Ivy to retreat and set up a defense if she makes a mistake. He'll be able to close the gap and punish her more efficiently on stages like that.
All things considered, if both players have their heads, Lucario has the advantage. He'll lose it if he surrenders center stage, approaches Ivy at the ledge, and gets gimped. Ivysaur will lose if she gets impatient and tries to force her will on Lucario, because she will have to play largely off of his spacing, and his decisions.