Does the shaft spin easily? Looks like it has ball bearings which is a good sign of a quality, heavy-duty motor. If so, I would focus first on powering it up. Replace the wiring, turn it on and hopefully a bunch of dust will just blow out from the motor's spinning. Most good motors have a cooling fan inside the housing.
Then, if it runs OK for a while (say, 15 minutes) without getting too hot to the touch on the outside casing, there is no need to dismantle and clean it. I personally would be eager to hook the motor up to the lathe and see how the lathe runs (I'm a woodturner). I am interested in seeing pics of the lathe if you would be able to do that