Cleaning those porcelain lids with a razor scraper is one of the most satisfying tasks you can do. Particularly on the inside -- the carbon comes off in long strips. The outside I did more with 0000 steel wool and Simple Green. The lids are glass inside and out, so it is really hard to damage them.
I have the same 2000 DD grill that Chris does. Here it is after removing 20 years of grease. Close to new.
Razor scraper on the inside/outside of the lid. Then scrub the thermoset (tables, knobs, handle) with bleach. Crazy how good those work.
PS to Chris -- are you the original owner of that grill? The firebox on mine was getting a bit bowed out. About two years ago, Weber sent me a brand new firebox -- lifetime warranty on the cast aluminum parts for the original owner. So that grill will now be passed down in my will.