He'd definitely come out best by just getting a transformer to drop the voltage. Chances are there's more than one motor on the machine unless the coolant pump, etc is driven off a PTO from the headstock like some of the old W&S turret lathes. Some machines that were built for 220V only, use 250V rated electrical components. To convert a machine like this, he'd need to go to 600V components which would cost more than a transformer and entail lots more work too. At the minimum, he'd need to find heaters for both halves of a likely obsolete 2speed starter. Finding heaters like this can be difficult, and people who have them don't sell them cheap. The machine may currently use a 110V control circuit, and if so, he's have to add a txfmr to get that back to 110V even if he did go to 440V on the motor. A rewind on a 2 speed motor isn't a cheap proposition either, and most any lathe that came with a 2 speed motor needs both speeds to have an adequate range of spindle speeds. My WAG is that he'd spend more on a rewind alone than he paid for the lathe.
In comparison, with a transformer, you hook up the 3 incoming leads, make the ties for the proper output voltage, and hook the output to the lathe. He won't find anything else that's cheaper, simpler, or less work intensive.