The thing about modern electronic drives is that they all start out the same way, by first making a high (ish) voltage DC supply from the incoming AC shop supply, and then the electronics artificially generates the voltages for the motor. All those that I have seen so far have available connections for 3-phase motors, but if in setup, you select a single phase motor type, they just use two of the three terminals. One becomes deactivated.
You should be OK on the 240V socket. AC electric is not magic, nor black art. The handy thing about 240V is that since the voltage is double the 120V, the currents are halved, and the heating losses in wires are quartered. VFD's are often 95%+ efficient. The inefficiency happens in motors, if of older traditional type, being run too slow.
An easy little walk-through is to start with the 2 HP. That would be when the motor is turning at the rated speed on the label. The horsepower unit has been well messed about with, but mechanically, is taken as 746 watts. So your 2HP means 2 x 746 = 1492 Watts. Loosely, think of it as about 1.5kW.
Knowing you have 240V, and Power = Volts x Amps, it's not too hard to figure that the current would be 6.21 Amps, but that is only true if everything was 100% efficient. Motors can be very efficient if turning fast enough, but expect it to want around 7 to 8 Amps from the socket when you are making it work hard.
I did mention that the VFD's rectify the AC mains to make a DC supply, known as a "bus". The VFD artificial 3-phase made from this may be a lower voltage version of 3-phase. If the 3-phase motor was originally wired in the higher voltage "star" configuration, it may need to be connected in the "delta" configuration. Your nephew electrician will be able to do this for you. As for information on exactly how, this site is stacked full of folk who know, end even more who did not know, but got to where they needed to be anyway, from the advice received.
You are right in that VFDs should be reasonably matched to the size of motor and load they have to deliver to. Things do get awkward if they are working on a small fraction of their designed load. Choose one where your load is about 80% of the capability.
A top tip is to exploit the gearing in your lathe when running slow, doing heavy load cuts. The torque from motors falls away as they slow down, and VFD electronics can run out of steam trying to deliver full torque from near a standstill in a traditional AC motor. It can be done with DC motors, and special AC motors of the sort in Tesla electric cars, but unlikely in a squirrel-cage AC induction motor from a year beginning with "19". If you use the gearing to have the motor turning as fast as possible, you will have enough speed control to have the chuck turn about as slow as you could need, with lots of torque.
I am in UK. The guys here will be able to guide you on USA available kit.
