I see Bruce Wayne being a threat to Clark, especially because he's this billionaire playboy, and he's totally macking on Lois.
You've got Lois doing some Daily Planet interview/piece on Wayne, introducing who Wayne is, his story (bam, cue the Wayne Murders - Bruce's life was cloaked in tragedy at a young age, blah blah blah, Lois interviews him about this, and we as an audience are "introduced" to Wayne). Lois and Wayne hit it off and they're a hot item; Clark is jealous.
Wayne has come to Metropolis to help rebuild the city ... but he's really there to investigate Superman. But he knows he could never fight him, because Superman is Superman - he'd kill Batman instantly.
So Wayne discovers Kryptonite, or maybe even creates it with his genius mind and billions of dollars: his one chance of leveling the playing field and weakening Superman so they can have a real fight. This is Batman's key to stopping the threat of Superman on the world and keeping him at bay.
Meanwhile, Superman is enraged to discover that Batman is actually Bruce Wayne, the guy who is totally macking on his would-be girlfriend...
... *Ding ding* FIGHT.
No Lex Luthor is even necessary here. It's a perfect, epic story.