You want to see crazy wheels, you have to see the ones from Tut's chariot. They couldn't have been made on a lathe. They took a series of v-shaped crooks and carved each one into half of two adjoining spokes and a portion of the hub. Then they bound pairs together to make the hub and spokes.

Spruytte, in Ancient Harness Systems, recreated these using copper rather than gold bindings. He also shows a number of ways to have spokes without the usual inset rods using forked and straight sticks.

I don't see why you need a lathe to make spokes or hubs, anyway. You shape spokes roughly then finish them with a blade held as a spokeshave (there's a reason for that tool's name). Hubs are drilled then shaped by hand around the hole, if you're not an Egyptian. It's slower than a lathe, but if there are no lathes, you don't know faster. You just work carefully to get it round.