Okay, thanks, Tom.

I actually have one of those on a drill press. I guess I meant, not what is it, but how would it work here since this is a toothed belt drive, and also the motor is variable speed DC, so I don't actually need a variable pulley ratio.
I was thinking about adding a countershaft only because I already have a 5 to 1 motor to spindle ratio, and I could probably use a 10 to 1 ratio to better effect, given this DC Motor. But that would mean making a giant pulley for the headstock. As a solution for something more wieldy, if I add a 2 to 1 countershaft to the present setup, that will have the same effect, and I will still have variable speed.
If I turn the motor end for end, and then attach a journal with spindle to the motor case, belt the two together, 2 to 1, and then put the original driver pulley at the other end, belted to the lathe spindle, that would be a simple and compact reduction power unit. In overall form, It would look like the motorized milling spindles people make up for cnc gantry mills.
BTW, one important need for a toothed drive is that the encoder for the electronic leadscrew has to sync to the lathe spindle. The encoder runs at motor speed if direct drive, or would run at at countershaft speed (if there is one). In either case it runs at 5x spindle speed.