There are many long, religious threads about lube in DMM rotary switches.
I'm experimenting with
Krytox GPL 105.It's basically liquid Teflon in a fluorinated-base. Used in Aerospace and MILSPEC.
No silicones, no petroleum, non-reactive, non-flammable. It's the best lube out there, but very expensive. Doesn't evaporate.
Oddly enough, it's used by car dealerships to stop weatherstripping from squeaking due to body flex.
Krytox 105 is a medium thickness oil and I think 205 is a grease.