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Kiwi Mink Oil. Castor oil also works good if you want to use a lube pad. And Alberto VO5 hair dressing contains enough lanolin that it ought to make a good case lube. So head to your drug store, and there are lots of ready-made high-film-strength lubricants.

You could also try gear oil, like for a manual transmission (do not use automatic transmission fluid unless you just really want a stuck case)