No I have not.
Two reasons for that -
1) the motor is running just fine.
2) the rumours that you should stop the motor every 8 minutes are exaggerated. It all (as you will know) depends on Load-On-chuck.
Are you sure the noise isn't coming from the bottom pulley - the Idler Pulley - the damn screw works loose and, so far, nothing I do seems to tighten it until it shuts up. I just give it a drop of oil if it starts chirrping and give it a turn or two with pliers.
If it IS the actual motor then yep, time to go with a replacement motor but don't discount that it might just need new Brushes - or a bit of TLC and a service.
I know a lot of random shit, but I don't know lathe motors. If your screw is working lose, can I recommend you tighten it as much as you want when it's literally ice cold? That seems intuitive, but I bet it really won't work; however, a mini butane torch in the right spots with tightening might actually lock it in place where you want it.
There's nothing like a like a screw that's constantly dealing with vibrations while also expanding and contracting with every use.
Just a thought. Not sure if I'm talking about the type of pulley you need for a lathe, but many solutions carry over.
Also, I agree with your load comment. Similar motors were used for woodworking tools, grinders, polishers, etc. and I've never actually seen one die in person. I've heard rumors about excessive loads my entire life though.
They probably are likely worth more in copper windings than as a motor, but they sure as shit are bulletproof.