I'd guess most VFDs will simply rely on the electronics to provide a lower voltage output, but regardless unless the motor is inverter rated (higher voltage insulation), then even a VFD running at rated voltage can cause insulation breakdown due to switching harmonics. You'd typically prevent that problem by adding a sine wave/sinusoidal filter after the VFD, however I'm not sure if you can get them designed for 110V.

Would I be right in guessing this lathe originally ran of normal 3 phase, and already has a step-down transformer for the turret?
In which case, I'd look at using a boost VFD (230in 380out), and adding a sinewave filter if you're concerned about insulation issues (although the transformer will be the part likely to fail, as they are very unlikely to be inverter rated).