You'll have to do a little detective work to figure it out. But first let me suggest that if there is no smoke from the motor then it is highly unlikely it needs rewinding and rewinding a motor is an expensive proposition anyway. It would be cheaper to replace it.
But back to the question. There should be information on the motor about how it should be hooked up for "high" voltage and "low" voltage operation as well as for clockwise and counter-clockwise running. Typically that information would be on a sticker attached to the motor frame someplace. Look on both sides of the motor to see if you see anything like that. It's also possible that it's on the back side of the nameplate on the end of the motor. It's easy to remove that to have a look and you'll have to remove it anyway to look at the wiring.
If you find GE's connection information you just need to compare how your motor is hooked up with what their information says. Internal motor leads are almost always identified with either plastic or metal tags or stickers.
Failing that, you'll need to look for some other source for information. You could start with looking for something like "GE 3/4 hp 115/230 volt connection diagram " on Google or any other source. That will give you some information about typical single phase motor connections and most manufacturers use similar connections.
Oh, and unplug the lathe before you start poking around behind that end plate.