SmithDoor, I would see what rating the lathe is meant to have - e.g. Motor power, speed, and look for a Permanent Magnet DC variable speed controlled motor and controller of the same Max power and Max speed. Don't go bigger, or you'll exceed something that is a limiting factor in the design of the lathe mechanics. - It's not worth the money buying a bigger motor that damages the lathe!
Bearings (mainshaft) are a limiting factor for speed, also "balance" within chucks, faceplates, etc.
Bed, slides and guides are limiting factors for "stiffness" = how heavy and how fast you can cut metal. If you can't work as fast as you want with the current lathe, then changing the motor won't fix that. Change the lathe for something stronger - maybe bigger. - Or risk permanent damage to your precision instrument.
Usually, the safety of the machine from damaging itself is guaranteed by the manufacturer, by the size of the motor. They will never waste money putting on a motor that is big enough to damage the tool. - so you shouldn't. They are experts (not me!) so follow their principles.
Bearings (mainshaft) are a limiting factor for speed, also "balance" within chucks, faceplates, etc.
Bed, slides and guides are limiting factors for "stiffness" = how heavy and how fast you can cut metal. If you can't work as fast as you want with the current lathe, then changing the motor won't fix that. Change the lathe for something stronger - maybe bigger. - Or risk permanent damage to your precision instrument.
Usually, the safety of the machine from damaging itself is guaranteed by the manufacturer, by the size of the motor. They will never waste money putting on a motor that is big enough to damage the tool. - so you shouldn't. They are experts (not me!) so follow their principles.