A suitable motor on a 3 phase supply will produce a better finish, because it runs more smoothly than a single phase motor, (each winding gets 3 impulses per rev, rather than just one).
A V F D varies the motor speed because it varies the frequency of the impulses.
A lathe, because it moves a tool across the rotating metal actually produces a helix.
On a finishing cut, it might only be 0.001″ (0.025 mm) deep, and 250 /inch (0.0393 mm pitch) but it will be a very shallow, fine pitch, helix.
A tool with a minute radius on the nose will make the finish even better
H T H
Howard