What you are noticing is a deposit of grease and smoke that collects during normal use.
During use, the grease and smoke vapors slowly oxidize into carbon and collect on the inside of your lid and other firebox parts. This deposit will eventually peel, and looks very similar to paint. The peeling normally starts in the center of the lid and spreads outward. It may come off in sheets or flakes, and is shiny on one side and dull on the other.
These carbon deposits are non-toxic. But you might want to regularly remove the build-up. Fortunately, the peeling is easy to remove. Simply brush off all loose particles with a brass brush before you start grilling.
To prevent future build-up, after every grilling session, while the grill lid is warm—not hot—wipe it with paper towels or a mild soap-and-water solution.