Lucian's standard build works because it reinforces what he does best: win short trades, quickly regain tempo, and convert that pressure before true late game. He is not looking for slow scaling. He wants immediate damage and enough continuity to replay several clean sequences.
Long Sword
Sheen procs on passive Lightslinger double AA after spell
Bonus range for poke and the Q-AA-E-AA combo
anti-heal via the doubles AA Lightslinger passive
Gluttonous Greaves
Quicksilver
Strengthens trades courts AD to dominate trades in lane.
Finishes with his double auto Lightslinger on enemies already weakened targets.
Attack speed to that his doubles autos Lightslinger hit more often.
E (Relentless Pursuit) dash triggers penetration on each reposition.