I have to ask: Why do you want to clean it? It is just going to get dirty, dark, dingy again.
But, to answer your question. You can hit it with oven/grill cleaner and scrub with the household SS wool pads. That is a lot of messy work and slow going. The other solution would be an angle grinder paired with a wire cup brush. Or less efficiently, a wire brush in a drill.
But, if you are just doing it as a clean up for a grill you plan to continue to use for personal use, then just clean any loose gunk and cook on. Like I said, it won't take long to get dirty again anyway. Let's just call that "Seasoning" inside the grill lid. Cleaning that out of the inside of the lid won't make the food cook better or taste better.