I move with the tool so it would seem sitting on a stool would limit movement and put a great deal more stress on the hands, wrists, elbows and shoulders. Maybe there are other things you can do to help make turning easier? Change the height of the lathe to a better position? Use thicker/softer floor mats to relieve stress on the back and hips? Turn the lathe to face you when turning bowls, either swing head or turn off the end of lathe?
As a last resort sitting would require an adjustment to the height of the lathe. I would think about a chair with wheels so you can move freely and get out of the way quickly if something went wrong.
I know there are wheel chair turners, so it's not impossible. And OneWay makes a lathe that is easy to tilt for sitting or standing.