People on here used to get their panties in a wad when someone mentioned grease other than 33ms (but those are probably the same types that still wear military issue underwear too).
Reality is there is no SERIOUS difference for a barrel nut. MS, white lithium, etc... whatever. All you're doing is trying to get a decent torque reading and make it easier to replace the barrel later if need be. Some will argue "well you don't get the proper torque reading unless you use the mil spec grease!", to which I say "umm, yeah... as if 30-80 ft/lbs is sooo exact, right?"
The other BS argument you'll hear is "well it will galvanize/rust if you don't use the proper grease!", to which I respond "umm, yeah... as if spark plugs do with aluminum heads?"
People have even just used synth oil without issue.
As usual, the "mil spec" way is not the ONLY way (nor always the BEST way). Any decent lube/grease should be fine.