The pictorial isn't all that helpful on the motor connections. I don't see any lead identification coming out of the motor as is connected at the white junction block. That is where they break out the windings for reversing. If they were tagged, where they weren't visible in the photo, it could probably be figured out, but in the interest of getting you going asap, disconnect the leads U1, U2, V1 as well as the PE ground connector. After verifying these connections match the picture in the manual, or taking your own, we can figure out how to reverse it should you desire.
On the new motor, follow this:
(for Reference)
V2 = T1
Z2 + U2 + V1 = T3 + T8 + T2
U1+Z1 = T4 + T5
Connect V1 to T1 on the motor
Connect V2 to T4 + T5 on the motor
Connect T3,T8,T2 together and isolate (use wire nut if you can)
Isolate U2 with a wire nut
Ground under a screw on the motor
If the lathe runs in reverse, swap T5 and T8 in the configuration. We can investigate the integral reversing if you wish, but we will need to figure out the white block. If you have a meter, set up a continuity diagram of it, and we may be able to see if the motor can be wired as the original. I have my doubts.