Which BCB Mug do you have? It sounds like you might have bought a Mk1 lid for a Mk2 Mug. The Mk1 Mug should be stamped:
NSN 721-3131
1995
BCB INTL LTD
I swear by the BCB Crusader Mug (Mk1) - there was a smaller, aluminium mug marketed as the "Crusader Mug" way back in the 1980s so I prefer to refer to the BCB one by it's military designation, the '95 Patt Mug.
The BCB Mk1 system is a great set when used inconjunction with a '58 Waterbottle and Millbank Bag. I've not tried out the Mk2 version, never felt the need. I use it on the BCB cooker, directly inside the edge of a campfire or in a small cooking fire.
But why buy a lid?
I carry a piece of foil in the same pouch which I place on the mug to aid boiling and keep out dirt/ash. Initially, I used kitchen foil but I've switched to thicker foil taken from a supermarket pie. Cut to shape about 1cm larger than the shape of the mug's top - or leave rectangular. Works really well, doesn't cost anything, doesn't melt (in normal use), doesn't jangle and takes up no space whatsoever. In emergencies, it can be used for other applications and it doesn't much matter if it gets damaged/destroyed.