I use this non-petroleum base WPL "Whistler Performance Labs" wet lube most of the year:
https://www.mec.ca/en/product/5063-5...ain-Lube-120ml
I've tried a bunch and this one has worked out well. I think folks often apply too much lube or apply to a dirty drivetrain and get goop build up. For my sturmey-archer hub gear bikes, I use synthetic 0W-20 in the hub (our car's tipple of choice so I always have some on hand) injected with a little syringe or oil can depending on the type of oil cap. Each hub gear seems happy, though all three hubs - the '53 four-speed, the '50 three-speed dynohub, and Mrs. Ged's '56 three-speed each have unique pawl ticking sounds.