My best guess is that's a 3-phase BLDC or AC servomotor (the distinction can be a fine one), one cable is 3 phase power U/V/W, yellow and green I'm not sure, perhaps a temperature sensor.
The other wire is "controlsupply", which is likely low voltage power and 3 Hall sensor outputs SA/SB/SC. This is used for sensing the rotor position for the servomotor controller to use for commutation.
Some reverse engineering skills and an understanding of motor control systems are needed really to figure out where to go next. Why not use the controller that came with the lathe? That might be easier to interface too, but watch out for the high voltages.