I intend to replace the motor on mine soon. I searched for a long time before I came to the conclusion you can't get a more powerful motor that fits in the hole for the original one, unless you go to RC model motors. They claim phenomenal power in a small space, but don't last long. However, in this application they would run well below rated power, so they might last a bit longer. I have never been able to get enough information on a possible motor and a driver all together to know what to buy. It's a bit frustrating as the RC crowd work in strange units, of LIPO cells and Kv figures. Some proper data on power, current, torque and voltage would be useful, preferably with some performance curves.
I have got a powerful brushless DC motor and driver that should eat the job, but it will need to be fitted outside the casing, roughly where the power supply is at the moment. That will mean redoing the belts. I will make pulleys for plain belts, as the toothed belts are so noisy. I'm also looking to see if I can devise a proper back gear for low speeds. I used to work with a mill that had it built into the final pulley, but that was a bit bigger than the Basic lathe. The motor runs up to 12000 revs, so I would gear it for that as the maximum speed. Allow for a 2:1 range on the speed control and have a second pulley for half speed, maybe another one after that, then back gear for really low revs. Then the aim is to put modern NC onto it.
It might take a bit of doing - it might never get done!
Keith