Or is his best build IE Zerks Statikk BT LW Banshee?
IE's pretty solid, though with Lucian he scales well enough with raw AD, abilities, and/or CDR you've got options.
He's probably the best ADC to max CDR with - so running CDR boots and abusing the Beat Stick into Ghostblade isn't a bad idea. Brutalizer is pretty OP all things considered, the build path to Ghostblade is easy to achieve during the lanning phase, and you essentially hit that ADC status with Ghostblade alone, where you generally need to get 2 major items to really feel the carry kick in with stuff like IE + Shiv.
Not sure I'd run on-hit with him though, seeing as on-hit is mostly attack speed based, and Lucian's double-hit passive is the only real advantage he has for that path.
Otherwise you're sacrificing the scaling of his abilities (and autos) by persuing on-hit for no good reason. I'm not sure I'd call that on-hit build an on-hit build though, as IE and LW aren't on-hit items in any capacity.