I would have to disagree with it not being able to be turned on a lathe. I have turned some very tiny things on the lathe and if done right a 1/8" by 2" would not be impossible. Very pointy sharp carbide inserts and very light passed with just a .001 or so spring pass. You would use a dead blow hammer or lead bar on the back side as you turn it down which will reduce the vibration that causes chatter. It's possible but not something super easy and on a manual would be even harder. You can do real thin stuff if you do face cutting. You work the face down in diameter and step back like .005 and do another face cut to diameter. This is much easier on a cnc.
But there is much easier way to do the same think. Turn two wheels and drill and ream a hole in each that is just under .125 and the press fit a 1/8" shaft into the wheels.