Oh, well, the Dynamat wouldn't be removable either. It is super sticky. It is like wrestling with tar.
I guess if you were trying to make a removable lining, or a test lining, you could first protect the lid interior with a layer of butcher paper, metale foil (tin, aluminum, or aluminium), or plastic wrap. The grocery store will have fancy parchment paper for baking cookies. You can even get it with a non-stick coating nowadays.
That would allow you to make a shell-within-a-shell sound deadening shield. Sticky tape could hold it inside the lid when you want it to stay put (when you remove the lid).
Sean