I have an AC motor on a wood lathe. The capacitor melted. the value of the Cap is 30 microfarads 300VAC. I can't find a start cap anywhere below about 75 microfarads. All the Caps that I find at 30 microfarads are listed as run caps. The manufacturer of the lathe no longer stocks replacement parts for it. If I get a 30 microfarad at 360VAC will I be ok?

 

Unless there is 'something special' about a start cap, I believe that any replacement cap of the same (or higher) working voltage should do nicely. If it were my machine, I'd go ahead and use the 360V rated 30uF cap.
The thing I'd question is, though: why did the original cap melt?? Do you have the right voltage available at the machine, or some other problem with the motor? Can you put a DMM on the windings to make sure they're not shorted out? Was there a power surge or something?

All told, tho, if you put a $1.50 cap in there and it melts again, oh well. And if the motor is shorted, you're not going to hurt it any more! But take a look around in there if you can for anything 'off', like smells, loose line cord, etc etc. When you fire it up, give it a good sniff for anything burning!
Good luck, let us know how it works out!