If I attack an occupied battlefield with both Lucian Gunslinger and Warwick Hunter, would the Lucian attack trigger enable Warwick's attack trigger?

Yes, you can. Both are "When I attack" triggers that fire simultaneously when both units gain the Attacker designation. Since you control both, you choose the order they go on the Chain (Rule 383.3.d). Put Lucian's trigger on top (resolves first) — he deals damage to an enemy unit at that battlefield — then Warwick's trigger resolves and kills all damaged enemy units there.

This is directly confirmed by FAQ #1361: the same sequencing works for Crackshot Corsair dealing 1 damage followed by Warwick's kill effect. Just note that Lucian's damage is equal to his Assault value — while he's an attacker, that's the stat bonus shown on his card.