I've rebuilt broken tabs like that with ABS cement and powder. I'm not sure if the lid is ABS plastic or something else but one could scrape the paint off somewhere in the inside and see if it's a black plastic. If it is, it's pretty easy to cut a piece of ABS from a black plastic pipe fitting from a hardware store and the black, gooey ABS cement in the round can from the same source. I used a sander to make up some putty by mixing ABS cement with ABS powder to a moldable consistency. All bets are off if it's not ABS but Honda's fairings are mostly made of ABS on the Goldwings and Silverwing scooters as well as many other models so maybe BMW did the same.
I bought a new one for the Sport at it was less than I thought it would be. Just under $30 Canadian - about $23 US.
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