Metal lathe for large disc

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A taper across the face of the disc or on the edge? Either way, it should be able to do it without too much issue with the top slide set correctly, a couple of bed and cross slide movements may be needed if traversing across the face of the disk since there probably won't be enough travel in the top slide to do 7" continuous.
My big one at work can swing about 20" with the gap out. How thick is the stock you're starting with as well? If it's only thin it might be bit more challenging!
It's across the whole face, 0.011 of an inch.

I'm not doing it as I wouldn't have a clue. Trying to find a shop that will but I didn't know what is possible on a normal lathe.
That's a very unusual small amount of taper, useless for a frisbee.

I don't think it's impossible though, it may be costly though to have it done for you.
Yes, a honing disc to sharpen clipper blades

Find a small presission engineers with a CNC lathe. Communicate to them clearly and concisely what you want doing, including the grade of metal etc. If you're not fussy, tell them that too. Let them know what sort of accuracy you want.

I do custom metal work for my job. Not applicable to your work at all, but the customers whom are easiest to deal with are the ones who spec things clearly, with notes about flexibility also.

And, of course, they get a better price than ones who don't give notes on flexibility, but just specify weird stuff, that they don't even understand why they want it (probably read it on interweb and thought it was what they needed!)