On the small lathe i have , similar size to your myford M l 1 ish as im guessing this is the machine you going to hang it on… I used the motor off one of those small hobby drilling machines. See machine mart ,item-Clarke cdp 5rb [ they were much cheaper a few years back , B&Q at one time were selling them £ 29.99 , which was tenner cheaper than the one i"d bought a few months before, so i bought a second , i figured that was an acceptable price for a motor ,couple pulleys ,pair of bearing ,and a drive belt an a few other odd bits ] These are capacitor run motors ,and yes as other folk have already said they Do run a bit HOT ! And i did wonder if that was going to be an issue ! So i thought i would really give it some , as in if its going fail ,best fail now. So i ran it dusk till dawn = a good 10 hours ,didnt even turn it off when i stopped for tea break [ it was a fair sized job , 6 inch dia by 9 inch long—the job was wood former for a small furnace barrel — also it was driving through the back gear ,and running power feed….it didnt fail!! it seems that when this type of motor fails its usually the the capacitor that fails …[ possibly cos one side of the cap is in contact with or very close to the hot motor casing, easily fixed ! Anyway point is machine mart have a spares department maybe the motor is available as a spare, might be worth giving them a try ,or maybe similar is available on ebay ? These motors seem to come 2 sizes 250 & 350 watt not much in it size wise the 250s a bit smaller, it was 250 i used, also the motor starts with the load off ,the way i rigged the drive, thought id at least give it a bit of a chance . bodge.
ps I know thats a long time to turn a wood former , But i really was trying to get motor to fail !