Is 
a good item to build on Lucian? I'm mainly asking because of the CDR and Rage passive, which, if my "theory" is correct, should work well in conjuction with Lucian's W. This is probably a stupid question, but I'll take asking a stupid question over trying it in game only for it to work horrendously.
JxG Shots2 votesThese are all the items that you can use on Lucian. It all depends on what you're up against. 
Whatevsman971 votesWell what situation would I use BC in?
Ionian3 votesWhen your team is full ad, and/or you already have a dps ad champion like Yi/Trynd.
JohnJonesy1 votesWhen the enemy team has a tank comp.
That armor shred is reaaaaaaal nice.
Dreadlocks2 votesBC is pretty badass on lucian because of how well he synergies with it. The easy stacks with his R or just Q passive Etc.. And my personal favorite, the 40% cdr build which could be any combination +5% masteries or 10% runes masteries. If you want to be more utility and have a lil more self peel I think BC is great.. in terms of high damage out put though you are better off with the standard ADC items.
TurquoiseYoshi2 votesThis just reminds me of a joke that I heard a while ago about a Lucian who built BC. His ally scolded him for it. Then the Lucian says "If you don't me to have a Black Cleaver, you'll get a Black Leaver." Then he left the game.
JohnJonesy1 votes[Rimshot intensifies]
Whatevsman971 votesNot gonna lie, the moment I thought of building Black Cleaver on Lucian, my first thought was "How many black jokes can be made out of this build."
50000000000000001 votesIt also works well with his ultimate, which will allow you to put on a full stack of black cleaver.
The Bearded Bard1 votesJust try it in game.
LegacyDAP1 votesTrinity Force is better
BluePolarizer1 votesBC is pretty damn good if you're going for 5 offensive items which is a good build against short ranged enemies and melees.
makes you very slippery and sticky against melees while still decently tanky.