This was inspired by reading the alternate Batman films discussion, which is still ongoing.
The idea is a little different. Warner Brothers/ DC comics does not produce a third Batman movie, which IOTL was "The Dark Knight Rises". However, they still produce "Man of Steel", and then a second Superman movie that does not feature Batman.
"Dawn of Justice" is still made after the second Superman movie, but some of the material that IOTL was in that movie goes into the second Superman movie. Lex Luthor would be introduced in that movie but he would not be the main villain. Finding a villain to fight Superman that is not Lex Luthor or Zod is admittedly a problem, but maybe Intergang could be used.
Warner Brothers then does two Batman movies and two Superman movies to build up the characters before bringing in Batman vs. Superman.
I actually liked "Dawn of Justice" quite a bit, but I thought it had too much crammed into the movie. Putting some of the material into a second Superman movie would have improved it. The Nolan trilogy was very good but had the opposite problem in that it sometimes drags. It might have worked better as two movies, or you just drop the weakest of the three altogether.
This would have improved the poor critical reception for "Dawn of Justice" since I suspect the main problem is that critics just found the whole thing too much to absorb.