Like Andy above, I last rebuilt an internal gear hub 50 years ago.
Aaron's Bike repair in greater Seattle has a great web page on internal gear hubs, they do a lot of servicing on them. Scroll way down for info:
https://www.rideyourbike.com/internalgears.shtml
If you had the hub apart like them, I would use a top-quality grease on the gears and outer wheel bearings (they use green marine wheel bearing grease, it helps seal out water), and a light oil on all the other parts (they use Phil Tenacious Oil).
If you don't have the hub apart, I would drip into the shifter hole in the axle, 75/90 gear lube, which is what they use in heavy duty manual transmissions, it flows great but provides a bit more lube for hard metal-on-metal things than a light oil. If ridden in cold weather, I might use a thinner oil like motor oil or automatic transmission fluid like Dexron, as the ratchet pawls and light springs may do better with that, not get stuck in if the lube gets thick. Some criticize the additives in those, and yes, you don't need a detergent additive to remove carbon deposits like engine oil, however, all of the above have "anti-wear" additives, also known as "high-pressure" additives, and tests of bike chain lubes show a lot less wear with lubes that have that additive (as opposed to 3-In-One oil which does not, for example). That's good stuff.