I will second what Rich outlined, Teco N3, Automation Direct GS3, Hitachi WJ200 are solid VFDs and a decent cost/performance with proven durability. They also have programing to prevent restart if there is a power loss. I would avoid VFDs shipped from China, if DOA or a warranty issue you do not have much recourse, and no tech support. There has also been an issue with some of the Hyuang VFDs missing there braking circuitry. The Teco's are ok, their current basic model is the L510 series, but I think the other VFDs mentioned above will give you better performance and more features that would benefit a lathe installation, the price difference is nominal.
A good inverter rated motor is also worth considering, you can over speed them to about 120Hz and maintain full Hp, you need to change your belt ratios. Most standard 3 phase motors are easily rated to 1.5X their base speed (so 90Hz), you want a motor that has a constant torque ratio of something like 10:1 or better. The Baldor IDNM358IT 1Hp inverter motor is a good choice, they come up on eBay, I use their 2 Hp version, but also the Marathon BlackMax and BlueMax series motors work well if you can get a good deal on pricing. All these motors are TENV, so there is no issues with low/high speed cooling, usual 3 phase motors are TEFC and there can be some cooling issues if run too slow or fast for long periods.
