Hi, If the motor is marked 240/440 volt or similar then an easy solution is to wire it in delta (240 3 phase) and run it from an inverter which would give you speed control -possibly useful when turning big bowls.
If it is 440 volt only then some digging around inside the motor for the point where the three windings meet at the star point and splitting these out into 3 extra wires to the terminal block and you can connect in delta mode as above.
The first is dead easy and inverters can be got on ebay - not as cheap as they used to be but patience can be rewarding. Digging in the windings is an acquired taste but if this fills you with dread then and the inverter route maybe a motor swap to single phase
As for the control gear - you could fit new 240 contactors or maybe buy replacement coils if the contactor is modern or lastly if you have more time than spare cash, rewind the coils. Not easy and only really appropriate to older contactors which are more accessible.
Finally spare parts for woodworking lathes are possibly best sourced via a ww group. There are some here butcher wood as well as metal but not many.
Consider joining this forum. There are lots of helpful woodies here.