It's a Lodge DO lid, ca. 1940s. Enameling of DO lid undersides was something done by Griswold (Clean Easy feature), but I've never seen Lodge literature showing they did it as well. Lye won't do anything to rust, and it and vinegar both tend to dull enameling. The pitting on the top looks like it spent a fair amount of time underwater or perhaps buried. Probably won't have much luck refurbing this one.