I think a lathe is not on lads unless someone can swing 16 inches in a 4 jaw chuck that can grip the outside of the rim.
There is no way of truing up a rim has a hop or a wobble.
It needs to be machined in a horizontal position.......
Would suggest clamped to a Mill table in a jig that spins and holds the shape of the rim so it's flat and round.
There is a piece of engineering equipment that is called a slot saw.....this will be the correct width
Just a thought