If you nor the tow company has never done this before you'd be smarter to use a Landoll, not a rollback truck.
Most single rear axle rollbacks start getting into skilled operator territory past a concentrated 10k lb load. Most heavier duty single axle rollbacks can haul 14K on the deck if they avoid scales, but it's not a sound rule for machine tools.
You can use a double axle rollback, but these are less common and a big PITA because the deck height is 4ft+
Landoll is like the Swiss Army Knife of moving heavy shit.
You will need good skates to do this. You will need to look at the machine and see what kind of toe jack(s) it will require.
Also, I have not moved that exact lathe, but have moved many small slant beds like it. They are have a different mass distribution than you'd expect. The headstock is not the heavy part. The X axis and turret are usually the heaviest part of the machine. That plays a big part in deciding where you place your 3 skates to move it. You need the weight reasonable distributed to move it easily on skates.