In the past, if you wanted to get the facts on what the Military used, you could go to the following site, and pull up the specifications listed below.
http://assist.daps.dla.mil/online/start/, go to “Quick search” For whatever reasons, the Bush Administration have removed these specifications.
I suspect it is because of "Security" concerns
If you read in the book “M1 Garand to M14 Rifle”, you will find that the military had a problem with the Garand seizing in wet weather. So the military purchased commercial greases, conducted a rain test on them, and found that Lubriplate 130 was the most acceptable commercial grease. I think animal fat was actually the best of them all! Then they wrote a performance specification around the material properties of Lubriplate 130. Anyone who could make a grease that passed the tests outlined in Mil-G-46003 was able to sell it as Rifle Grease to the Military.
Military Rifle Grease is basically a NLGI 3, water resistant, bearing grease. I do not see any reason why a good grade of Marine Wheel Bearing grease would not work equally as well.
Rifle grease is meant for a hot wet environment. And is not meant to be used in temperatures less than 32 F.
I really like LSA as an all weather overall lubricant. VV-L-800 also is a good lubricating oil for rifles if you read the specification.
As for commercial oils, I have used synthetic Mobil 1 5W-30 Motor oil for decades as a lubricant. Just rub it in on an oily patch.
I think the easiest advice to follow, that I was given as a novice, for M1/M14’s was to use LSA in the winter and rifle grease in the summer. But as long as you use an oil in the winter, and a grease in the summer, your Garand will not have any lubrication problems.
The lubrication requirements of rifles is not that mysterious or complicated, and you will find many industrial or automotive greases and oils that will work. But most importantly, keep it lubricated!. Your rifle is a mechanical piece of machinery and needs to be kept clean and lubricated!
MIL-G-46003, Grease Rifle
VV-L-800 General purpose lubricating oil
Mil L 46000 Lubricant, semi-fluid (Automatic Weapons) LSA.