I have a Noma 27" 2 stage and wondered the same thing. Owners manual says Auger gear box is factory lubricated for life (page 16). Page 35 shows a complete breakdown of mechanical parts and shows it to be a simple worm drive. No mention of what type of lubricant though.
I did a little internet searching and Jack's small engines lists Murray part number 333431 as "grease for gear box" for Murray snow throwers. Outdoor distributors describes Murray part number 333431 as Lubriplate GR-132.
From the Lubriplate website:
"LUBRIPLATE GR-132 is a lithium combination type thickener, NLGI No. 1 grade lubricant with an ASTM dropping point in excess of 430°F and a workable cold test of -40°F. The light viscosity mineral oil in LUBRIPLATE GR-132 makes this lubricant ideal for many high speed applications where fluid friction must be kept to a minimum. The makeup of this product is such that it is compatible with a wide range of plastics."
I don't know if any of the site sponsors can supply Lubriplate GR-132 but a warning in case they can't: The Murray part number is priced at double the retail value of Lubriplate GR-132.