My normal build is Grieves-Bloodthirster-X-Last Whisper-Infinity Edge-Guardian Angel
In the X slot goes either Youmuu's, Statikk, or TriForce
They all seem like good items on Lucian to me, but which one is best?
The Chin2 votesI like yomuu's
Player of Games1 votesPhantom Dancer for the highest single target burst increase, Yomuu's is a bit lackluster in that slot now, and TriForce would be less DPS considering you're lacking a crit item other than IE.
So all in all, Phantom Dancer is superior for that imo. There's still nothing wrong with Shiv though, just PD offers much higher single target burst.
Reynard the ƒox1 votesI've switched over to getting PD on several other ADC's like Caitlyn and Jinx, but on Lucian I still favor Statikk because of the burst it adds to his spell rotation.
Aratez Treaty1 votesDue to his passive, 
is good, for ADC's in general, see if the team is building some armor (they should, but some don't). If not, another free item, so don't get 
. I generally start off all ADC's that I play with 
. Then go 
, and maybe, if you want to be more sure in the Crit's, Phantom Dancer, you may not really need it though. I do not do 
on any of my ADC's. Instead, get boots depending on your situation. Because you are laning against the other ADC, I prefer 
or the 
for the extra attack speed, look at your build, and your needs though. Situational. You shouldn't necessarily need 
. If you are good enough not to die in the first place, and if you have another damage item, while they build a , you should kill them first, and then, you can run/kite/bait for your team to help finish them off again if you are low, or they could be helping in the first place. 
, could be good if they do not build armor, and probably advised instead of or 
. Definitely have one or the other, but you probably don't need both, because an , , and , will net your Crit to 70%. If you had instead, it would be 75%, so the 20 armor pen. is probably worth it.
Remember that 21/9/0 are advised for that extra health, so that you actually exceed 2000 health points as an ADC.
Yuki Akuma1 votesYoumuu's gives him a bunch of stats he actually uses well. Armor pen, CDR, Move speed, attack speed, crit, and damage. No reason not to get it really.