Need some more info. What lathe do you have? Motor specs? Variable speed? If it’s just a plain ol’ AC cap. start induction motor check the bushings. Worn bushings will not allow the rotor/stator to self-align (clearances are TIGHT!) and will cause similar “locked-rotor” symptoms. You can live with quite a bit of end play but NO up/down slop! Start cap? Yes-it’s only for starting. Must be a pretty stout motor. Look for that cap. leaking oil/goo and/or any evidence stuff of getting hot. If the switch were funky you’d
probably smell it. Check for a voltage drop at the motor. There are no brushes. Those motors usually last a LONG time.