I feel more strongly about Maggie Sawyer going over to Gotham than I do about any villain getting spread around, Luthor included! But alright, I'll give it a shot.
General Zod, Mongul, Hank Henshaw, Conduit, Toyman, Doomsday, and of course, Doctor Lex Luthor.
I'm viewing this question in entirely restrictive terms, not liberating ones. This is about decreeing that Green Lantern cannot use Hank Henshaw as a villain if Superman isn't there, not about decreeing that Superman has to use Henshaw more often. That would change my whole list, and probably Yellow Mask would be at the top. I don't feel the need to restrict Xa-Du or Vyndktvx to Superman, because I don't see writers using them for other characters. I don't see the need to restrict Metallo or Parasite to Superman because, well, first of all they're really heavily associated with Superman so they probably don't run a huge risk of losing that association to other heroes anyway. Brainiac is big enough to just have Superman and Supergirl as his "arch" enemies and still fight others here and there.
I was iffy about including Luthor, after all, my favorite Luthor story is "Satisfaction" from the Young Justice cartoon, and the hero is Arsenal, not Superman, but ultimately I think that Luthor is too crucial to Superman to lose, considering that I really do think he might be becoming big enough to become a "Vandal Savage" who's a villain to the whole DCU instead.