Dont really think this is going to work robin, lathes are normally run by induction motors which would have a speed of either 1400 or 2800 rpm.
The washing machine repulsion motor will run at something like 30,000 rpm you would need a speed controller to accelerate to this speed gradually,or hold it at lower speed, it would be too fast to run full power from a standing start. You could not use the washing machine controller because it would only hold the top speed (spin) for about 6 mins and also would repeatedly reverse rotation on lead up to spin. Just an observation would be interesting to hear from others on this. Cheers
Kenjo
June 2012