Over the years wherever I've had the need to lubricate things I've
used automotive speedometer cable lubricant.  The kind that I use
has a graphite base and also has something in it to prevent it from
migrating.  The purpose of that is to keep it out of the speedometer
head where it could cause problems.

I've also used the powered form of graphite that is obtainable from
some of the piano technician's supply companies.

Hal Davis