Your explicit question relates mostly to the lens's mount, and David has answered that question. I'll add that some very old or weird enlargers have used mounts other than the usual M39 mount. Some enlargers have interchangeable lens boards, so they can use oddball lenses -- you'd have one lens board for an M39 lens and another for another type of lens. There's also the question of the length of the lens's "neck" -- lenses vary a bit in their lengths, and this can cause problems if the bellows (or other focusing mechanism) doesn't get as close or as far as the lens requires. I've seen this issue with some Soviet/Russian 50mm lenses, which can't focus properly (particularly for smallish prints) on some Western enlargers.
Some other answers relate to the coverage of your condensers. This is an important consideration, since if your condensers don't spread light evenly across a larger format, you'll get vignetting in your final print. I don't know enough about your Omega enlarger to give you any specific advice on this matter, though. Note that this issue is entirely unrelated to the physical lens mount issue.