A VFD can drive a 2-speed motor (I have one driving a 3-speed, and had to hack it to deliver 415v from 240 and do some devious programming to get it to work), but it's not at all simple to do - a rotary convertor is a lot simpler to implement, unlike a VFD (where you will need to modify ALL the lathe switchgear to operate the VFD's start/stop/reverse etc.), a rotary convertor is pretty plug-and-play, just wire / plug the lathe to the generated 3-phase and use the existing switchgear as the maker intended. Also a rotary convertor will let you buy all those tools that are cheap because they're 3-phase and most hobbyists only have at best 220v single-phase in their shops - just plug them into the convertor, away you go!
The motor in that lathe is probably 400v only, if so you may need a transformer to get the voltage it needs, an old stick welder with a dual-voltage transformer can do that pretty cheaply, then for the convertor you'd need a 400v 3-phase motor (with more horsepower than the lathe's), a couple of contactors and some run capacitors to balance the phases - your nephew may be quite capable of building it for you, efficiently and safely?
Dave H. (the other one)