Stan writes:

I picked up a used glass pot lid, the kind with a metal band around
the edge. The glass has cooked-on grease on both sides of the glass
and I can't get this slightly-sticky-in-places residue off. What's a
good way to get the glass on both sides clean and free of that
cooked-on grease/fat?

Spray oven cleaner or old fashioned lye. Unless the metal is aluminum,
then use a non-lye oven cleaner, such as one using ethanolamine.