League of Legends (LoL) Question: Lucian runes and build

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.

You should be taking either Triumph or Overheal, Legend: Bloodline, and Coup de Grace. For secondary, you can take Sorcery with Celerity and Gathering Storm or Inspiration with Perfect Timing and Future's Market.

For your build, there is one popular build with many variations:

1. Blade of the Ruined King > Black Cleaver > Essence Reaver > situational

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.

Other items you can buy are:

Blade of the Ruined King > Black Cleaver > Rapid Firecannon/ Phantom Dancer

with situational items for both builds being

Mercurial Scimitar Bloodthirster Maw of Malmortius Infinity Edge Lord Dominik's Regards Mortal Reminder Guardian Angel Death's Dance Edge of Night Youmuu's Ghostblade