Lazlo was a waiter who worked for Fish Mooney and one of her lovers.
Lazlo was the victim when Don Falcone sought to teach Fish a lesson about her place within his crime family. As Fish's current boy toy - Mooney told Falcone explicitly that he is not her "lover" - the Mob boss had two of his goons beat up Lazlo publicly in Fish's bar whilst he himself lectured her on loyalty.
Later, Lazlo asks Fish if she is planning on any more actions against Falcone, voicing his concern for her safety. Fish appears to be touched, but then orders one of her men to dispose of Lazlo, feeling he lost his nerve.