Well given Clark Kent looks exactly like Superman minus the glasses, has an iron friggin' chest that goes 'clink' when Lex taps it, nearly crushes Lex's hand, and is talking to a billionaire playboy from Gotham named Bruce Wayne who oh so happens to approve of Batman's methods... I'd say the way that scene is shot, acted and written implies Lex - at the very least - is pitting the civilian identities against each other.
That and the whole 'he doesn't know who they are' thing kinda undermines Lex's intelligence just a little. What, he's going to reverse engineer a Kryptonian into a monster but can't work out Clark Kent minus glasses is Superman?
ETA - Also, Lex hates Superman. I always assumed if Superman fucked off and lived a quiet life as Clark Kent, Lex wouldn't give a shit about him.