Make targeted changes to him and everybody else.
Personally, I think Lucian should have his point-and-click Q removed and replaced with a skillshot piercing Q instead. One of the big problems a lot of carries have versus him is the fact that you have to account for both (a) a double auto from his passive and (b) the outright burst from Q. I believe making the Q a skillshot would make him much less annoying for many without taking away his overall identity.
Besides that, I think other carries need to have a more pronounced strengths like Ashe being the #1 kite-flier and Vayne being #2 pentakill montage poster girl after Katarina.
Let's take Graves as an example. I would rather his Q deal damage to a target multiplied per bullet instead of a just % increase. This matches the whole shotgun theme he's meant to have going on. Hell, Explosive Shot should deal double damage to some motherfucker if you hit them point-blank.
Riot has said before that every champion should have a moment/situation/scenario where they feel absolutely OP because the stars are fucking aligned and it's their moment to shine.
If you wanna talk burst, Jinx is just as good and has more range, Corki can burst you and still poke after while dealing true damage each hit.
If you wanna talk utility, Lucian's dash is better and he doesn't even need AS because of his passive, Vayne has true damage + hard CC + AD steroid w/ stealth, Kog can shred HP, Trist has healing reduct + reposition + self-peel.