Assuming the machine can turn freely ...
Is this a single phase ( 240 volt ) machine ?
If so, sounds like a start capacitor issue - simple fix, replace the motor capacitor .Cheap and easy - and it's the most likely cause.
If its a three phase ( 415 volt ) machine -
If there is a DOL starter, it might be that the contactor is only bringing in two phases. The motor may not start - especially under any load conditions - but would run once the motor is turning. If so, replace the DOL
It might be worth checking the resistance between each phase and checking the winding insulation ( using a mega ) i.e resistance between each phase and earth. This would normally show up any major motor problem.
Usually machine tools have sufficient power to overcome any minor lack of lubrication and you would probably hear the machine "complain" before you had a motor issue.