As has been said already, the 3-phase motor needs to be dual voltage (220 / 415) for it to work with any decent torque when powered by a 'basic' inverter (somewhere around £100 new, for around 2HP motors). If the motor is not dual voltage then you could buy a 415 volt inverter, but they are considerably dearer. Alternatively you could have the motor rewound. This is what I did for my milling machine. It was not actually a rewind, they just delved into the winding and picked out the necessary wires to allow me to connect to them. This work cost me about £30.
As to whether you would benefit from 3 phase - yes, definitely. I have a Myford ML8 which I have converted to 3 phase and the variable speed advantage is sooo worthwhile - especially when turning uneven / unbalanced timber. I still lose some torque at very low speeds but I can live with that. (Actually it's quite handy because if I get a dig-in on jagged baulks of timber then the motor stops safely.)
I have a 3-phase motor ready to fit into my own Union Graduate, and am looking forward to the upgrade.
Bear in mind that a replacement single phase motor will just do one job - the lathe - whereas a 3-phase inverter will power the lathe plus any other equipment you may buy (within the capacity of the inverter, of course). My inverter powers my milling machine, my ML8, my new surface grinder, and soon ( I hope) my graduate. When I acquire another 3-phase motor I shall change the motor on my old Myford ML4 metal lathe as well. I don't need to change any parameters - I just plug in a different motor and it works.
If you decide to buy a single phase motor, you could probably sell the 3-phase one on this forum to recover some costs - I'm sure there would be plenty of interest. (Or ebay, of course) but carriage could be more that the cost of the motor. However - personal opinion - I would definitely go 3-phase.
K
