a 1/4 hp motor would be sufficient to run the lathe
my suggestion (easy way, not much else is needed than belt and pulley)
56 frame
1/4hp
shaft diameter 5/8"(standard for 56 frame)
1140 RPM
that being said,
i have read that there was a small flaw in the design of the lathe.
the spindle runs too fast with OEM sized pulleys for most operators taste.
most folks run 1740 or 1725 rpm motors on machine tools.
a motor speed reduction to 1140 rpm would be a simple and effective means to achieve a slower spindle speed,
using the OEM sized step pulley.
(only if you were inclined or worried about higher spindle speed- a 17XX rpm motor would work too.)
if you have the desire and means, (cool way, but more intense set up and learning curve if not familiar with electrical installations)
why not make the power plant a 56 frame, 1/4 hp, 1740 rpm motor, 3 phase, and add an inexpensive VFD to control the speed ????
inverter rated 1/4 hp motors are dang cheap these days, and the even the inexpensive VFD's are quite reliable.
there is also the option to run a DC motor(also cool way, less trouble to set up than 3phase/VFD, but more complex than simple single phase motor set up)
treadmill motors are quite inexpensive, and can be used
there are also commercially available 56 frame DC motors too in 1/4 hp that run on 90VDC.
MC40, MC60 , KBIC ,and other inexpensive PWM controllers are quite capable of being utilized as well.
if i can help out, send me a message