How do I choose an appropriately sized stepper motor?
If speed and acceleration aren't a problem, then there are two other mechanical performance issues you need to get right. One is the torque. You should measure the amount of torque required to turn the dials on your lathe while making its deepest cut into steel. You're a mechanical engineer, I'll leave you to think of a way to measure it.

Take a look at the datasheets for the stepper motors you are considering, and they should have a speed / torque graph:



You can see that this motor's torque just about peaks at 0.8Nm. But at this torque, it can barely move. Obviously you wouldn't use this motor for any torque duty above about 0.5Nm. Select a motor which has plenty of torque.

The other issue is the resolution you need. Again, it's up to you to decide what resolution you need, and what your lathe is really cable of. Stepper motors are typically 200 or 400 steps per revolution.

If 1" takes 8s, and the motor is rotating at 0.8RPS, then one revolution gives 0.156" travel (is this a metric lathe?). For a 200 step motor, each step gives 0.78 thou travel. That's pretty good actually. If you used a microstepping motor driver, that will essentially increase the resolution. You should do this anyway, even if you don't want the extra resolution. The microstepping will prevent the motor suffering from the resonance that happens at certain speeds.