I have used 3 mm thick foam, >1/8" - don't make it thicker since the foam is used only to prevent the leather sticking to the painted metal.
Glue the foam to the metal, not to the leather, and I believe that it does not go all the way to the outer perimeter.
Use a mister and spray some distilled water on the leather inside and stretch it around the curve. You can use a hairdryer and carefully heat up the leather when secured in place to get out small wrinkles.
P.S. make sure you use high-temperature foam, those lids can get very hot in the sun!