From what I have been told the plastic lid was designed so that vehicle crews could turn their MOD plastic mugs into "sipper cups" and avoid having their brew spill if the road was rough....not sure if it is true but it is the only use to which I would put the plastic lid!
When using it on the metal mug I have had the plastic lid jam tight (due to the metal/plastic expanding at different rates in the heat?) making it difficult to stir my food with a burned dinner as a result.
I made an alu lid for my metal mug by drawing thearound the cup rim onto a block of MDF to make a form, then battering a sheet of aluminium over the form with a ball pien hammer. The sides were levelled on my belt grinder and a hazel button handle fitted. Later I drilled 3 small holes in the lid to make it double as a strainer when prepping pasta/noodles/rice.
The first attempt was a bit "rough" but the second is in regular use.
Neither model took more than half an hour to make
version 1