Failing nail polish remover and paint stripper, a bit of warm water and gentle, sideways-nearly-parallel to the glass scraping with a razor blade should get the laquer off.
It's quite a satisfying sort of thing to do.

Back in the '70s when these were popular, Beswick made dangly siamese cats to hang on the rims, with a little mouse to sit inside the glass. The mice nearly always seem to be missing, this glass would hide the lack of mouse! I have a spare (mouseless) cat if you'd like it.