If this is the only thing that you expect to have in the shop that is going to be 3phase, then go with a VFD. They are less expensive both to buy and to power over time.
If not, I would look closely at a RPC.
Now there are some truths to an RPC that many don't know or forgot, that I will let you in on.
First is starting power.
The starting power of an RPC is directly related to the STARTING load of the equipment that you are running.
Meaning that if you are trying to start an air compressor, fan, winch (with load on) or other motorized device where the motor you are starting is expected to immediately see the full rated mechanical load of the motor you are trying to start then yes, you need 1.5 to 2 times the size RPC of the rating of that motor.
SO, you have to ask yourself, are you going to be starting the lathe in the highest spindle speed it has, with a cutting tool buried in the material being cut?
Of course the answer is NO.
So does the lathe have a clutch? If so, it gets started with little or no load.
We already decided that you will not be starting the motor with a tool against the material being cut, so again, not full load.
Now you will need to consider that if there is no clutch, and it has the clausing belt variable drive, you CAN'T run the speed down with the lathe not running. SO, there is some loading to consider that will differ with the spindle RPM setting at startup so we are still looking at a minimum of a 1 to 1 ratio.
Personal experience.
I have started 20 HP motors with 10 HP RPC's with the 20 HP motor sitting loose with nothing on the shaft to test the motor. It was never an issue.
I have started 40 hp motors with a 15 HP RPC. Again, no load, no issue.
All RPC's I have or have had are fully balanced. Meaning that I had run caps on both the L1 to L3 and L2 to L3. This is what is referred to as a "CNC READY" RPC by the manufactures. Basically it gives a leg to leg voltage a balance within 10%. Running caps on L1 to L3 or L2 to L3 and not both will decrease the starting and running ability of the RPC. Or decrease it's rating. But of course it's also cheaper to build.
Now, mind you I am a pro RPC kind of guy. But I run welders, plasma cutters and other 3 phase stuff that require 3 phase and the normal VFD stuff will not cut it for that equipment. I also build them to fuel my home machinist addiction.
All that being said, I have also run my Clausing with a clutch and variable speed with a 7.5 motor off a 5 HP RPC I built to see if it would run it. I was in back gear, and I was turning about 110 RPM on the spindle, but I was taking a .125 DOC (depth of cut) off a mild steel bar. So it was loaded, and it didn't complain, but it did chatter a bit thanks to a loose gib.