Thread is a bit old, but I think it's still relevant especially with the recent Shiv/PD buffs and the RFC nerfs.
First of all, a little clarification about attack speed and Lucian's playstyle/passive: attack speed is actually very important, because his passive IS auto-attacks, which are linked to attack speed. What I mean by that is that animation-cancelling is a lot faster/easier with attack speed and if you aren't animation-cancelling his combos your DPS drops significantly.
Also, the current style of ADCs isn't really based around burst dmg, which is what Triforce usually serves as. And why I think it is a waste of gold right now.
1st item Essence Reaver - pretty badass, gives him lots of AD and he really needs the mana regen, because of all of his combos. Not to mention the all-important 40% cdr that you're itching for.
2nd item RFC - as I mentioned, you really need attack speed to more easily animation-cancel, also it increases your DPS drastically. And that range proc is broken beyond belief.
2nd item Shiv - Statikk Shiv got buffed and it looks pretty good on paper when it comes to split-pushing. However, i really dislike what you get from that item compared to what you get from RFC as the range passive from RFC is very good to have in almost any situation, unlike Shiv's proc.
This is my core build on Lucian (and some boots which i'll talk about later on), because the rest really depends on the particular game.
Even though I'd love to get IE 3rd item I rarely have the opportunity to do so as I usually end up needing QSS or Bloodthirster's shield/lifesteal a lot more.
Those 3 items are basically my choice for itemization from that point on. I'll usually get all 3 of these items in a different order, depending on which one I need the most. Unless I don't need QSS at all in a particular game.
Also, another item to consider is Black Cleaver, the shred and utility (movement speed) it provides is very good in most games, where you usually end up playing against a 10/2 tank/bruiser toplaner. I would never recommend getting Last Whisper/Dominik's simply because as an item it is very inefficient and on top of that, specifically on Lucian, The Black Cleaver straight up outperforms it by a mile in comparison.
Boots - ah, simple, but tricky! If I'm getting Black Cleaver at any point in the game I go for Berzerker's Grieves, if I'm not I get Lucidity Boots (you still overcap CDR with BC, but it's fine).
Also, I used to love Ghostblade on Lucian, because how the active synergized with his ult and how the flat arpen synergized with Lucian's bursty combos, but since the meta's shifted quite a bit and Ghostblade's active got nerfed I never bother with that item. Not to mention they removed the crit from Ghostblade and you easily cap/overcap CDR without it anyways.
BotRK is another item I'm not really talking about as it's in a really bad state right now in general, even though it's relatively easy to proc the passive dmg a bunch of times with Lucian's Gunslinger passive. The lifesteal on the item is a joke and I just never end up getting it mainly because of that. It still has its uses and it might've won me a few games, but yeah...the item's just underwhelming right now.
Summary - Lucian is the top dog once again, I consider him the best ADC by a mile at the time of this post and that is because of the current ADC itemization giving him easy access to insane amounts of AD, crit, attack speed and max CDR. I do expect Lucian to get seriously nerfed again real soon (they just nerfed the range on his ultimate). However with all these options, despite having lots of games on the champ, I still often find myself losing games I could've carried, because I built incorrectly in a particular game. Having so many options just gets a bit too tricky sometimes. ALSO 500 RANGE, i'll never forgive Riot for that!!! :)
As always, when it comes to itemization - everything is a subject to change. Champs get nerfed/buffed, items get nerfed/buffed, playstyles (metas) change, so take everything with a grain of salt.
