Perhaps Brainiac could "infect" Lex like in the JL cartoon so that he survives when Superman defeats him at the end of the first movie. But then, anything that Lex does from that point on would be attributed to Brainiac and he would not get his fair share of character development.
I would only go down that road, after Lex has had his share of development and screentime, and after a big confrontation/discussion between him and Superman with blood in the water, sharks coming, chips falling down, people eating each other, etc. In other words, about the 3rd or 4th movie. Only then would i surrender Lex to Brainiac and of course i would never do that freak-horror show that we saw in the JL. He would just be Lex with superpowers, his eyes flaring up when he uses them, and he would have a more Brainiac-esque voice once his infection is revealed and he can no longer hide.
And since this subplot was part of the wider CADMUS arc of the JL cartoon, i'd love to see all this in a movie one day (i mean the CADMUS arc).