Interesting! in Bill Jones’s books (the last ivory turner who did remarkable precision work for chess pieces etc.), he describes his lathe that was run by belts, he had a foot pedal to slacken off or tighten them to give him control of the power coming from the motor, which he thought was critical to good turning. IIRC he thought that modern lathes had little’feel’ compared to the belt-driven ones.
Trying to be helpful; the pot (potentiometer) will just be a resistance change or voltage drop (probably resistance) detected by the lathe’s electronics. A simple computer like an Arduino or Raspberry Pi could mimic the signal, and take an input from a variety of sources including pedals.
The other thing that springs to mind is guitar and keyboard pedals such as volume control, you may be able to find one with the right spec that would be a direct replacement for the pot (possibly swap it for a 1/4” jack).
This then brings up a question of whether you want it to have a spring-return force (you step off, and it stops), or you position it and then leave it.
My only concern would be that for small things like chess pieces this might be a good idea, but for things a few inches across and larger I find I move my weight from foot-to-foot to maintain a smooth cut, so controlling a pedal on larger work may be difficult
Good luck!