For a lathe application, stick with the Clausing variable system. A Lathe needs lots of torque for big turning, tapping etc. You will not get that with a VFD alone. I have a RPC to convert to 3 phase, works fine, I installed it in the garage but the noise finds its way into the workshop anyway. A VFD is almost silent, uses no power at idle, and is cheaper to purchase, and use.
To use a VFD from single to 3 phase, you need to purchase a unit double the size of the largest motor it will run. IE: 1 hp motor needs 2hp VFD, the controls of the lathe On/Off FWD/Rev need to be controlled by the VFD, not the motor controls on the lathe. A 5914 is a vary belt drive not HYD as far as I know. This is fairly simple to do for anyone familiar with electrical wiring, all controls would be low volatage through the VFD.
I had a VFD on a SB 16 Lathe, it was necessary to shift the belts for enough torque for the large D parts, and running taps and dies. The 1944 vintage motor did not blow up at 50% overspeed, but I was uncomfortable with pushing it higher. Slow motor speeds are what invertor duty motors were designed for, as it causes great heating of the stator windings due to the frequency used in VFDs
about 15K hz, so non invertor rated motors could fail at continued low speed high load conditions.
If this will be your only 3 phase machine, go VFD, if you might ever get a mill or grinder, then a RPC makes sense, of you would need a VFD for each machine.