I don't think you can take Lois out of Superman. I mean, she's not like Batman's random romances or Iron Man's or even Spider-Man. She is integral to the Superman mythos, more so than any Superhero romantic interest. To me, she even rises above romantic interest. In many ways she is Superman's equal and at the very least, she's his partner more than any other really.
Lex has to be in this too.
Lex has become more than the archenemy. He has become an integral character in the Superman mythos along with Lois, Jimmy and Perry. It is important to have him in the movie, but just keep him as the supporting character. It is time to let another villain shine.