I use MILTEC-1, synthetic metal conditioner grease!

It is a very modern synthetic lubricant designed for military use in all kinds of weather conditions.

MILTEC-1 Grease stays in place and lubricates in the severest conditions.
*Has excellent water wash-out resistance.
*Has superior shock-load protection
*Reduces corrosion, wear and galling

This product comes in a small 2 oz squeeze tube that fits well in your fitted case, or in a day pack. I have a tube in every one of the fitted cases for all my doubles, and always have a tube along on any hunt! I buy this from LONG GRASS, in Texas, as they keep it in stock but it can be bought from the maker I suppose!