The title refers to Batman, another DC Comics universe superhero.
The Superman clone is described as bizarre by Lois. This is a reference to the Superman villain Bizarro, who first appeared in Superboy #68
(October 1958).
The Clone refers to Luthor as his father and Luthor treats him like a son. In DC comics, Superman was cloned using a digital representation of his genome and the full genetic information of a human man: Lex Luthor. This clone was Connor Kent a.k.a. Superboy who debuted in the wake of Superman's death at the hands of Doomsday. For all intents and purposes, Superman's first clone was in fact Lex Luthor's biological son.
Clark's mother suggests parallel universes as an explanation for the Superman imposter, which Clark dismisses. In DC comics there actually is a multiverse, consisting of countless parallel universes, with many having their own Superman.