Haas recommends Mobil SHC630 synthetic oil in their rotary indexers. Its not too viscous, but that suffices for worm gear drives that barely get warm while in operation.
Browning has a very heavy weight worm gear lubricant, IIRC, about 140 weight or more, pours like molasses at room temp. That would be for a really hardworking gearbox that gets hot.
It may be an interesting bit of trivia to know, but a single start worm has the highest coefficient of friction (resists backdriving), and more starts may prove to be better in some instances if speed reduction is the primary concern, where heat buildup may otherwise be considerable. Logically enough, a large diameter worm also has a higher circumferential velocity, so this may also generate more heat through both stirring action and worm velocity.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)