Reply by Kazooman

I can’t tell the dimensions from the pics, but if that ridge is very high you would need a really long shaft on the router bit. I also wonder about supporting the piece while you work it.

Perhaps the rough shape was made by a series of rip cuts on the table saw with increasing depth to match the curve followed by hand scraping. That would give you good support during the machining. It appears that the handle is centered on the lid so you could make one cut, rotate the piece to cut the other side, raise the blade, adjust the fence, and repeat until you had the maximum depth. Then the waste could be cut off the face of the lid.

I imagine that you could take a card scraper and grind it to the desired curve profile, sharpen it, and then have the smooth curve in no time.