I think this will work, and it doesn't require any special tool set up, other than what we already have. It's complicated; I'm sure there's an easier way. We could use a round nose bit to cut the semi- circle channel.
First, machine the lid, but don't cut the center hole; just leave the drilled hole in the exact center. Then, decide how far in from the edge of the lid you want the channel to go. Set the fence, or just clamp a fence, on the router table this distance from the bit. Then fasten the center of the lid to the router table; the easiest way I can think of is to drill a pilot hole through the table and put a small screw through the center hole in the lid; loose, just to keep it in place. Then, set the bit depth, slowly lower the lid onto the bit, and just rotate the lid along the fence. The screw keeps the center of the lid from "walking"
Matt