For my TS I went with a TECO VFD and a VFD rated TEFC motor. Not the cheapest option but solid. Good tech support too. After a few years the VFD died, probably lightning. Of course the replacement TECO was a little different but works well.

A motor only provides one level of torque and can stand rpm turndown to about 30% for a proper motor. And cooling is reduced. For a lathe which needs to deliver full torque at high and low speeds for long run times, keeping the motor at or near full rpm is best. And a wide speed range is needed, more than 30%. So mechanical speed reduction is required. Reeves drive or belt changes combined with a VFD is good.