In something that moves as slowly as the tuning machines on an instrument, the problem usually isn't lack of lubrication, but dirt and heavy oxidation.
I disassemble and clean mine about every 10 years or so. I've had it since the 60's. For a while I used a graphite gun lubricant which worked pretty well.
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Bill Bentgen http://www.billbentgen.com
Pöllmann 5 String Bussetto 1999
Kay C-1 #24190 1950
Sue Lipkins German Bow 2011
Prochownik German Bow 1999
Flexocor Strings
Pops Rosin