The likely spec for the OEM motor on the lathe is probably 1800(~1740), a 4 pole motor. What will be needed is the rated "base speed" of the DC motor. It most likely has a 'permanant magnet' field. . . Then you must figure in the installation of a speed controller, either on install or some(possibly remote) time into the future. With a 'PerMag' field, you cannot easily overspeed the motor. I don't know your particular machining circumstances, as a rule I would try for a ~2400 or so RPM at base speed.
The reduction arrangement of multiple belts/pulleys may well serve several functions. Direct drive from the motor to the spindle is not recommended. Motor torque will fall off dramatically at speeds below 40-50% base. You will need to keep the motor speed up to some nominal speed and use the belts for reduction. Older machines were basically designed to be run from a line shaft, the speed of that source would have been much lower than an electric motor. Even then, there was a small reduction between the drive and the spindle.
The desired pulley sizes will be a ratio rather than absolute sizes. Figure the size of the OEM pulley. Then, knowing the base speed of the DC motor, find a pulley, either larger or smaller, to give a similar speed on the first stage of the countershaft. Making the allowance for above base speed as desired. That should get you started, it may be necessary to adjust the drive pulley up or down from there.
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