I believe there are two ways to level up Lucian. You will always be maxing Q first, and then you can either choose to max W or E next. So let's talk about the strengths/weaknesses of these two paths.
Of course, you will be leveling up your
at levels 6, 11, 16 for the more dmgs.
First, I'll explain why
should always be maxed first. At max rank,
has a 5 second cooldown, which means every 5 seconds you will be able to use your passive. Not only that, but
is your main wave clearing ability so maxing this ability will let you wave clear much faster. Not only that, but out of your three non-ultimate abilities,
will also scale the hardest from the AD you will be getting throughout the game. These reasons are more than enough for every Lucian player to max Q first.
Personally, I recommend going for the
? This is because putting points into
will make your burst skill combo deal more damage, as well as lower the cooldown on the ability. The only thing you benefit from leveling up
is decreased cooldown, which at max rank is at 10 seconds, and the mana cost. To me, I feel like similarly to Corki who has a very long cooldown on his escape ability Valkyrie, Lucian should treat his dash ability similarly. As long as you're able to pre-position yourself well, one dash should be enough for you to survive along with Flash if needed. I'd rather much prefer the extra burst that comes from
because not only does it help waveclear, but a lower cooldown on this ability means the more chances you'll be able to use it to kite aggressively/defensively using the movespeed bonus from the skill.
means you will have increased mobility, but that's the only reason. Remember that your dash resets if your ultimate kills something, so to me if I cant get that I'm still gonna have to wait an incredibly long time for my dash to come back again. So personally Id rather pay attention to my positioning harder so that I will be able to dish out more damage, while still keeping my self ready to change positions.