There are a few good Lucian guides out there, but Vapora Dark has a very nice Lucian Guide which has explanations for how to play as an ADC as well.
The best keystone rune on Lucian is Press the Attack because it only takes two auto attacks to activate it if you have Lightslinger up. It's also the best rune to take because it lets you play more aggressively during Laning Phase, which Lucian will want to do because of his level 2 powerspike.
BoRK and Black Cleaver have insane synergy with each other due to the armor penetration and %HP damage it provides. Essence Reaver will make it so you can use Relentless Pursuit more often after you use your ultimate, which is a great thing to have.
The best keystone rune on Lucian is
You should be taking either
For your build, there is one popular build with many variations:
1.
BoRK and Black Cleaver have insane synergy with each other due to the armor penetration and %HP damage it provides.
Other items you can buy are:
with situational items for both builds being