It's time to buff Lucian. Professional and Amateur stats agree. My suggestion for how to fix him.
At the end of Season 4, Lucian was taken out back and beaten with the nerf bat until he reached his current state. He was taken from the must pick ADC status to his currently borderline playable position.
Here are just a few stats to show where he ranks in comparison:
Summer split NA LCS: 0/1 0% win rate Summer split EU LCS: 0/4 0% win rate Summer split KR LCK: 5/13 38.4% win rate Win rate from champion.gg Plat+ games across all servers: 45.91% 18/18 among ADC Play rate from champion.gg Plat+ games 21.76% 3/18 among ADC Win rate for summoners with 125+ games(Lucian Mains): 46.7%
The stats speak for themselves, Lucian is in a weak state right now.
I believe that Lucian does not need a major buff in damage but instead some help in the movement speed department. Here are my suggestions and reasoning.
Buff base movement speed from 335 to 340. Lucian is designed to be a highly mobile in your face marksman. This buff will give him the maximum movespeed in the game for champs who have ranged auto attacks.
Additionally, Lucian's W contains a movement speed buff. ACTIVE: Lucian fires a shot that explodes in a cross pattern upon hitting an enemy or reaching the end of its path, dealing magic damage, marking enemies hit for 6 seconds and granting Jens Ingels LoL- Sight1 standard sight of them for the duration. MAGIC DAMAGE: 60 / 100 / 140 / 180 / 220 (+ 90% AP) If Lucian damages a marked target with his basic attacks or abilities, he gains movement speed for 2 seconds. This does not consume the mark.
However, due to the fact that a spell or auto must be used to proc this, he must already be within range (500 for AA or Q) or dash in or use his ultimate to proc the ability.
My suggestion: Remove the need to proc the ability. Change the W to apply the movement speed bonus on hit for the 2 seconds. This will allow Lucian to either move in to range quickly without using his dash or to aid in his escape and kiting from all of the dive heavy tanks. In its current state the W is mainly just used to proc his passive or to close the distance or kite while using Lucian's ult.
Overall these changes are aimed to allow Lucian to be a part of the teamfights and also chase people in lane without having to use his dash and flash while still maintaining his identity as a highly mobile up close ADC.
TLDR: Buff Lucian's movement speed abilities