SAMS
Local air superiority might need more than a few fighters and, presumably, some assured sea control would be required for carrier ops. Wiki mentions that Libya has SA2, 3 and 6 so some good ISTAR and hard/soft counter measures would be required. I think it would be fair to assume that Gaddafi (or however you spell him today) would be more than happy for his AD assets to be weapons free. I'm thinking that AWACS, AAR, SEAD/EW, Recce and pre and post fighter sweeps would be pretty essential for starters. If carriers are involved, add some ASUW and ASW airborne assets. Given the distances, you could probably protect the land bases with QRA but that would likely not be responsive enough to give cover to an up-range carrier.