The best option would be to use a single phase motor with the same RPM's.
More torque might sound good but also means in moments of "OOOPS I missed it" damage can happen to parts of the lathe that would otherwise have no problems.
Easiest way to check the CAP is with a tester, either in a multimeter or with a dedicated tester.
You can't see from the outside if these Caps are dead, if in doubt invest the 10 bucks and replace it, but double check that you the right size for the motor.
Wrong seize, e.g. 25µF instead of 10µF can mean the cap does not like it or the motor can overheat.
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