It's an Albion gearbox. Royal Enfield had a love affair with Albion that stretches back for years and years. The routine Royal Enfield advice was to fill the gearbox with whatever engine oil you were using at the time. Albion boxes never used grease. Always used oil.
That said Royal Enfield also advised the following about oil leakage from the gearbox.
"It is sometimes found after a big mileage that some oil leakage occurs from the driving side of the gearbox, or from the bearing for the kick starter shaft. A simple and permissible method of preventing such leakage, or reducing it is to substitute a mixture of equal parts of SAE 50 oil and medium grade grease for pure engine oil."
So there you are, oil only and when you find it leaks like a sieve , a mixture of oil and grease. Logically, no fancy expensive stuff but the cheapest oil and grease you can get because you're going to use a fair bit.
Cheers,