Hi Mark
If yours is a single phase machine it sounds like it could be a fault with the centrifugal switch in the motor or the start capacitor which that switch puts in and out of circuit on starting. As a rough check try taking of the primary belt, from the motor pulley to the clutch and quickly spinning the motor pulley by hand while switching on to see if the motor will run once it has been given a bump start so to speak. Worth checking that the lathe itself is running freely, I know someone who forgot about the spindle lock pin at the rear of the headstock. Give that a try for a start and if you post your findings more help can be given.
The start capacitors are fairly robust but do have a finite life, fortunately a cheap repair, if you do spin the motor up, turn the motor off and listen for a gentle click as it slows down,this will tell if the centrifugal switch is working mechanically, testing electrically will be more involved but fairly simple, see how you get on and report back.
Good Luck!
Edited By Dave Wootton on 23/09/2023 07:47:44