I use LSA55 military weapons oil and no grease. I figure the Army tested it well enough to be a quality lube.
The only grease I use is Ponsness- Warren STOS on the hinge pins of shotguns
I'm not familiar with that one. The LSA I see referenced in the TM and such is a relatively heavy oil for light machineguns and heavier automatic weapons.
LSA stands for "Lubricant, Semifluid, Automatic weapons." and it is mentioned in the FM-3-23-35 for the M9 and M11 but only not to mix it with CLP.
The spec can be downloaded as a pdf here
MIL-L-46000 C LUBRICANT SEMI-FLUID
Here's one manufacturer of oil that meet the current milspec.
Mil-spec Lubes | Weapon Lubricant | MIL-L-46000C | SENT-46000
There were lighter gun oils used before CLP, for various small arms. Toward the end of WW2 Special Oil, Preserving and Lubricating became used for both normal temperatures and cold weather. Grease was applied to specific points in the Garand, and for better protection from rain on the carbine - but for the carbine only in that situation.
edit: The curent version of that is
"MIL-PRF-32033, PERFORMANCE SPECIFICATION: LUBRICATING OIL, GENERAL PURPOSE, PRESERVATIVE (WATER-DISPLACING, LOW TEMPERATURE) (24 JUL 2000) [SUPERSEDING VV-L-800C]., This specification covers one type and grade of water-displacing, preservative lubricating oil,..... The oil is identified by Military Symbol PL-S and NATO Code Number O-190."
Bottom line. I do think your logic is sound that the military spent some effort in selecting or specing oil that provides lubrication and preservative functions. Just pointing out that one is more for severe high pressure and heat uses.