The only problem I would expect in a lathe is the difficulty in securing the plate to something and holding it perfectly flat while cutting so it doesn't flex and get some thin spots or let the cutter dig in and rip the whole thing loose. That's why I was thinking of a grinding fixture. It might turn fine if you could figure a way to hold it.

ccjersey is right about trying to turn the disc. If you could find a machine shop that has a Blanchard grinder, it would be a snap. A Blanchard grinder has the faceplate (chuck) running horizontally and the grinding wheel is also running horizontally and the faceplate can be moved from side to side. If you're in a fairly populated area, a machine shop having one might not be too hard to find. Most shops have a good idea of what each competitor has as far as equipment and capabilities.