Lucian's Problem
I think the single biggest issue with Lucian (and the reason he's been left in the gutter for so long) is that he suffers from a serious identity crisis. What is he supposed to do? What does he offer that no one else does? What are his strengths, and perhaps more importantly, what are his weaknesses?
Straight up, imo, Lucian is just a worse version of Graves currently. His trade pattern is to dash in and blow his high damage burst abilities on a target and disengage or all-in from there. There's a bit more micro management with his passive, but essentially it's the same play pattern, though arguably even better because of the drawn out spread of guaranteed damage from his passive double shot. At the peak of his popularity, he was in fact just a better scaling Graves. He had a great early laning phase, solid mid game, and scaled decent into late game, with no real distinguishable weaknesses to punish other than maybe his low-ish attack range.
So Graves is the definitive champion for bursting a fool down at point blank and being tough guy, we can safely establish. Lucian has two guns. But he isn't the first adc with two guns, that would be Miss Fortune (who definitely needs work herself, and not what Riot is doing to her on PBE). Miss Fortune will forever reign in my mind as the Queen of AoE Teamfight Wombo as far as ADCs go, from back when her Ultimate actually had AD scaling (which I will argue it desperately needs again). But what does Lucian do? Based on what abilities Riot has given him and tweaked over the years, I'd say he should ideally fit into a mobile close range single-target face-melter, and not in a burst fashion like Graves, but with a rapid onslaught of attacks shredding his enemies to tattered pieces. He should probably be a better close range duelist against squishy targets than Vayne, at least damage-wise, since she is built around tankbusting and often out-duels other damage dealers using her cc and stealth.
Personally, I don't think Lucian will ever be a healthy champion while his play pattern centers around poking from range with the massive damage on Q. I think that ability makes a lot more sense as a point-blank kind of skill, maybe with reduced damage to targets further away. Currently it just consumes too much of his power budget imo. Even his passive took hits for it, and his passive probably SHOULD be his central trading tool.
Likewise, his W is pretty much only useful for proccing his passive. I'd personally like to see more utility shifted onto that, like a larger movespeed bonus that is refreshed when attacking an affected target, rather than being a one-and-done buff. Lucian should be a nimble champion who favors in and out trades, with serious chasing power for finishing kills, as well as allowing him to reposition more rapidly in fights. Additionally, I'd like to see better interaction with his Ultimate, to promote some actual kit synergy. Specifically, if his ultimate shots could proc the movespeed from hitting targets affected by W, allowing for superior chase and kiting. Additionally, to cement its use as a utility skill rather than a damage ability, it could trigger a debuff on enemies that when autoed repeatedly, ccs them somehow? Like a short root or stun, but it takes like 4 hits or more to do it. I only suggest this because the unfolding shape of the skill is very reminiscent of the trap box from Ghostbusters, which I assume was an intentional choice considering Lucian's background and theme. So it should be able to trap an enemy in place to take a face full of ultimate. I'm kind of imagining an effect similar to Viktor's Gravity field when the cc is procced, pulling the target into the deployed W. This could also open up some big plays by chaining his w, ult, passive, allowing you to potentially group up enemies for a big Q to the face.
His E was probably the most fun and synergistic when it had a low cd that was lowered further still by using his passive on champions. Being able to actively dash around fights was very cool, though breaking slows might have been just a little too much. I haven't played him much lately, so I dunno if it still interacts with his passive. I just think that was one of the best changes made to him, since it promotes what I think really should define him based on the concept of his kit, an in-your-face but just out of reach kind of guy, not unlike Vayne.
Returning to his ultimate, I think it is currently terribly out of place. The damage is much lower and harder to hit than just continually autoattacking, and so it's a poor choice for close in fights, while nothing else in his kit promotes a playstyle wherein you would attack opponents from far away. The range just doesn't fit, and the damage doesn't feel rewarding for the time and effort it takes to use the skill.
I remember hearing his ultimate was very briefly tested as proccing on hit effects (not sure if this included crit) and was determined to be extremely broken, but was it tested that way with a much shorter range? I really like the idea of the rapid stream of bullets blasting down foes, but I think it makes more sense as a last ditch get-out-of-my-face-kid use-case. That is to say, more damage, less range, and lifesteal for clutch duels? Not sure about letting it crit, but that would allow for a more crit attack speed build. I like the idea of it having damage comparable to a bunch of actual autos blasted out in a short space of time, balanced by the difficulty of landing each individual shot as a skillshot, but what sounds fun can often be entirely broken. That's just my two cents on the kind of thematic direction I think it should go in. I definitely think that Ultimate shots should proc lifesteal, just because of the duelist role his kit seems to suggest.
Namamall has suggested dividing his ult into segments tied to "charges", allowing Lucian to proc his passive more frequently (and consequently get in more dashes), as well as allowing him to better fulfill his "Two-Guns" fantasy, being able to actually shoot at different targets more rapidly while dashing towards targets and away from danger. Big shout-out to him, as that could in fact be the best change for making his kit more thematically cohesive and fantasy-fulfilling.
I rather like the idea of the charges working as a mix of Ahri's and Akali's systems, where you have a window of opportunity to spend your other charge(s), and can get more charges and an extended duration from kills and assists, but once that window is up, the ability goes on cooldown. That way you have a window of vulnerability as well.
Anyway, TL;DR: Lucian needs for Riot to decide what it is that they want his kit to do, and he needs them to make his kit synergistic within itself to that end if he is ever going to be both viable and balanced. His problem has always been that he is too good at everything and not too bad at anything.
You'll notice there are no numbers attached here; this is because I'm not a mathematician. Just some ideas and observations. Let me know what you think down below.
+
meta to allowing other adcs to be played. Blame season 4
HELLO?
and AP lucian broken. Lucian was nerfed to the ground because of how much power he had in his kit, making it so basically anyone could play him, suck, and still stomp his lane. Right now at higher levels, his ability to Q poke is what lets him win his laning phase. Once it ends, he plays essentially the same as the old lucian, just he isn't as over powering unless you got fed in lane.