Lathe C -Axis

Yes, it shouldn't be too hard. I nearly managed it with an ordinary induction motor spindle.
You might want to decide if you want to use it as a full C axis, or use M19 spindle orient.

Well, first you have to decide on how you want to switch between C-axis and normal spindle control.

One way might be to always drop back to C-axis closed-loop when the spindle is turned off. That could probably work, but might make getting the chuck key in difficult, or clocking up work in the 4-jaw chuck. So to make that decision requires consideration of how you expect to work. (Those considerations are irrelevant with a power chuck and bar-feeder.)

If switching that way then I think I would be looking at writing a custom HAL component that feeds the PID with a target position 2 full revs in the future when the spindle speed drops below a threshold.