If you need the extra power, it's hard to beat the price. But i think the 1/2hp motor might still have a lot of life left in it. There's a good chance it's a simple fix. The start capacitor may be shot, or it may have a lot of sawdust packed in it which is fouling the centrifugal switch. If it's a Repulsion start / Induction run (R.I.) motor, you may also have worn brushes or a fouled commutator. I'd start with the no-cost option - dirt. Most older motors are "open" with vent holes in the motor housing. This helps cool the motor, but also allows in sawdust and dirt.
The refusal to start spinning at all makes me think it's an induction motor (no brushes) with a fouled centrifugal switch, or a Repulsion start/Induction run motor with starter winding issues - probably the brushes. There could be other causes, but these seem the most likely to me, and they're easy to ferret out.
Since it's a lathe, the motor is probably either a capacitor start induction motor or an R.I. motor. You can tell the difference easily by looking for the telltale cylindrical tube (the capacitor) attached to the motor. Without that, it's probably an R.I. motor.
If you've never had a motor apart before, it may sound intimidating, but they're pretty straight forward. And, if it's already not working, what do you have to lose? The cleaning process, start to stop, should take 30 to 90 minutes. I'd start by marking the location of the rear bell housing to the main motor housing - marker, metal stamp, tape, etc. so that you reassemble things correctly. I'm assuming you have the motor on your workbench and unplugged. Remove the bolts or screws that hold the bell housing in place. On a motor that size, you've probably got 4 to deal with. I like to make sure there's enough clean space on my bench to lay out removed parts in an organized manner. Take pieces off carfully and set them asside deliberately so that you can reassemble everything in its proper order.
Once the bell housing screws are removed, you'll need to tap the bell housing off of the main housing. They're still held together with a friction grip. I like to use a wood block or broad flat blade screw driver to begin to drive the pieces apart with light taps working around the perimeter of the motor so that it all comes apart without wracking and binding.
Once the rear bell housing is off, you may be able to easily remove the armature (assuming you've already removed the pulley and any heavy dirt/corrosion fouling the shaft as it comes out of the other bell housing. If it comes out easily, remove it and set it aside. Now, you'll likely see decades of dirt packed in. I like an old toothbrush and a small paint brush or two to go after the dirt. Be carful poking anything rigid in there - you don't want to damage wiring. Once i get a good enough view of how things are arranged, i'll usually use a stick of wood to scrape off the large chunks. Occassionally, i'll use compressed air, but turn the pressure down to about 40 psi and wear eye protection. You may also inspect the centrifugal switch at this point to make sure it's clean and can move as it should along the shaft of the motor. There are different configurations, but they're pretty obvious to figure out when you're looking at them. Also, look for cracked, broken, or missing parts on this switch. There are springs and weights to account for. Any damage should be readily apparent.
You'll also want to take a minute to inspect the wiring connections to make sure things aren't cooroded or broken where you wire the cord to the motor. I'd also check the bearings to see that they don't have too much play or make any grinding or chatter noises.
Once it's all cleaned up and you've inspected the other items, reassemble the motor and give it a test.
I've "resurrected" a number of motors just with a good cleaning. Once i had a centrifugal switch that was sticking - a little cleaning brought it right back. The rest of the times, just getting rid of the dirt took care of the problem.
If the power cord looks iffy at all, i replace it. It's not always necessary, but it's only a few bucks, and there's no easier time to do it.
If things don't come back to life, take the capacitor with you to a motor repair place or an industrial supplier (Grainger, McMaster Carr, etc.) - they will test it for free before selling you a replacement. My last capacitor replacement was $7 - not expensive and easy to swap out.
I hope this helps some.
I hope others look this over to see where i may have left something out or may be missing something.
Have fun with it.
Paul Hubbman