Here is an update to an old thread.
I think many backpackers use a small titanium mug. These have various sizes, but it is not uncommon to have one with a lid that is about 4 inches in diameter. Most of these lids are titanium, although a metal lid here is overkill, weight-wise. The lid is not exposed to direct flame temperatures, and it is exposed to steam.
For my mug, the metal lid was 3.8 inches in diameter and weighed 15 grams. I fabricated a lid out of carbon fiber sheet to beat that.
First of all, you can online buy 4"x4" samples of various carbon fiber sheets at Protech Composites. That 4 inches may be a deciding point, since they don't seem to have samples much larger. For thickness, I got samples at 3.1mm and 0.5mm. All I can say is that the optimum thickness would be either 1mm or else 0.5mm. The 1mm would be rigid, and the 0.5mm would have a bit of flex, rather like stiff cardboard. I decided to run with 0.5mm. Carbon fiber sheets are pretty inert to anything like steam.
I traced out the top of my titanium mug onto the 0.5mm carbon fiber and cut it with ordinary scissors. After sanding the rough edge a bit, I determined where the center was, and that is where a tiny handle was needed. I did not want a bulky handle, and I did not want one that might stress the center of the carbon fiber disk. I wanted a handle that was (1) lightweight, (2) somewhat foldable, (3) somewhat heat resistant, and (4) it still had to be lightweight.
I took a 1-inch piece of silicone string, held it in a loop, then wrapped a bit of small gauge insulated copper wire around the bottom of the loop. The wire holds the loop shape. Then I used epoxy to glue the wire down onto the carbon fiber lid. I used both wire and silicone since the epoxy would hold something firm like wire better, and the wire would anchor the silicone string better. I felt like silicone string would wiggle loose from epoxy directly. The net result of the lid with handle is a bit less than 5 grams. Maybe 4.8 grams.
I agree that aluminum foil might weigh less, but it is not very robust and not very stiff. One advantage of aluminum foil is that you can fold it up tighter for transport.