For the moment I'm ignoring 'on the cheap'.
I can't see how you could use it as a 4th axis and also as a 'lathe' with the same drive motor.
What about if you used it as a 4th axis with a stepper motor via Mach3, you would not need any braking in this instance and implimentation would be easy.
Then when you want to use it as a lathe you could use a cheap standard induction motor driven by a vfd, the vfd would provide variable speed and dynamic braking with ramp down.
You would just need a simple way to swap from one drive motor to the other.