Rolling around with a heavy and unequally balanced machine such as a lathe is a risky business. Agree with the skates and Johnson bar or screw jack with a lifting claw. If I had to do the forklift option I would only lift enough to clear the trailer and pull the trailer out. Then lower the machine directly onto the moving skates. You can rent skates, Johnson bar, etc from local equipment rental stores. At least I can here since there is a demand for that kind of thing locally. Not sure about your locale. Buying skates, etc are an option. Good to have for future moves. I'd buy a set myself but they sell quickly around here when they rarely come up on craigslist.
Your tilt bed trailer will work but you have some rigging and unloading issues you have to be prepared for. Too much to type since I'm lazy. CALL me and I'll talk you thru it.
Chris