Ah, so it's not just staining. My mistake, I thought that it was staining after you'd gotten the crud off.
The powdered brewery wash will really help soak that off. No idea what it'll do to the staining, but it'll help shift the stuck on stuff. I know I've used it for the plastic brewery tubing, but I don't know about the Norgie lid plastic......up to yourself on that, but if it were mine and the lid was so badly caked up, I'd give it a go.
I don't know if it's the same as the Bar Keepers stuff that Mesquite suggested.