As mentioned earlier, you can run a 3-phase motor on a single phase, but you have to have a means of starting it- e.g. pull start or capacitor- and it will only run at 2/3 rated power. There is a technique for wiring the third leg via 'run capacitors' as well as 'start capacitors' so that the motor will operate more smoothly (another form of white-man magic) but I think this still produces 2/3 rated output.
My 3hp lathe motor is actually running on a VFD rated to 2hp that was given to me by a friend. Not an issue in general use, but would not be able to run at full load such as heavy cuts on large diameters. I'm running it off a 20 amp circuit that I had installed for my welder. A lot of VFDs require 3-phase input for 3-phase output, something to watch out for if buying. One of the things with these gadgets is you can program all sorts of running parameters such as spool-up time, gradual slow-down to stop, emergency stop which uses electrical braking, forward & reverse, speed control etc.
I'm not by any means an expert in the subject, just did a bit of reading and internet research for my own purposes. I don't know how the current draw would compare between the various arrangements. The reading I did made it pretty clear that having switches between the VFD output and the motor input would be detrimental to the VFD, my understanding was one motor, one VFD.

