I don't want things to be typical at all.
Lex going full throttle on the villain gear.
The way I see it, he should still dislike Superman, but see Batman as more of a threat at this point.
Lex is a criminal, and Batman is a crime fighter.
It would put the scares on him surely?
Superman and the rest have no idea about what kind of dark secrets Lexcorp holds, Lex himself.
Possibly not even Batman.
Lex could hire assassins to watch over Batman and take him out at some point.
It would serve Lex's interest in all regards.
Deathstroke and Lady Shiva would be cool. Compensating for Zod and Faora.
Slade Wilson could even potentially want to make enemies out of Superman, too. Say he's still in the Army and disagrees with Stanwick.
Josh Brolin and Rinko Kikuchi are my picks for those respective roles.