Lucario feels fairly even to me, and I fight dedicated Lucario mains pretty consistently. Both characters have to commit for their kills, Lucario even more so, and while he has a projectile that on paper forces Falcon to approach and low lag aerials that make it fairly difficult, Falcon does have the speed to do that efficiently enough. Like in any MU, you should pressure Lucario with feint approaches either by canceling dashes with a shield, rolls or extended dash dancing. Throw in some nairs, uairs and bairs here and there, but avoid actually approaching as much as you can. There isn't really much Lucario can do from a distance until he hits higher percentages. Dash attack, shorthop, jab and generally everything is an answer to aura spheres until then. Mid range is where Falcon wants to be, it's close enough for Lucario to be unable to react to a dashgrab and too far for him to do anything until his side b lasers get more range with aura.
Once he gets the aura going he can sort of gain the upper hand in neutral with his lasers and aura spheres. When Lucario is charging an aura sphere, more often than not they'll try to pressure you with it rather than instantly release it. If so, just dashgrab them. If they keep shooting it, dash in, shield and punish. It's a 50:50 situation that you shouldn't be respecting too much, the aura sphere won't realistically KO you. Watch out for Lucario's empty jump command grab, and avoid shielding in close range because of it. It commonly kills even Falcon at 50-80%.
When you're getting up from the ledge, Lucario can charge his aura sphere to eliminate all of Falcon's getup options. Ledge attack, regular getup and jump all result in Falcon getting stuck in the aura and rolling onto the stage will let him shoot the aura sphere at you on reaction. If you drop off and uair him, he can shield it and then punish your next ledgegrab with aura sphere. Hence, you should drop off the ledge, uair him and immediately up b. If he gets hit by uair, you get back onto the stage for free. If he shields, he will either get grabbed by the up b or evade it giving you time to grab the ledge again and quickly get back onto the stage. Sometimes you can not uair at all, instead just jump off and bait him to shield, then either up b or just regrab the ledge and jump back onto the stage etc. Mix it up creatively based on Lucario's habits and it's not a huge problem.
Now when you do get the advantage, stay in on Lucario as much as you can and don't give him the time to breathe. This is how you should ideally play the whole MU; mid-range pressure, minimal shielding and constant harassment. This minimizes Lucario's chances to play with aura sphere or command grab you, hence gaining advantage. Lucario's close-range options are fairly limited and he can't keep up with Falcon's speed. When he's offstage, force him to use his up b and try to intercept it with dair, and as time passes, this will become easier and easier. You'll need Lucario to be at around 40-50% for it to KO him because of the length of his up b, and Lucario can adjust his trajectory to avoid this but in most situations it will result in him experiencing coffee break level landing lag which you can punish with at least Raptor Boost, even if you went for a dair and missed.
Lucario's fair can pretty much exploit our lack of horizontal reach in the air (I've noticed that this is actually one of our greatest problems in many matchups), but well-timed bairs are still good.
Yeah, Falcon uses his hand for his back air and only half of his leg for his fair. Uair is pretty good though, it covers like 180 degrees around Falcon, starting slightly below the mid-horizontal level in front of him and ending somewhere slightly before the mid-horizontal level behind him. You can actually use it to escape some combos.
