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Any lubricant will work just fine for installation of a barrel nut, because you are just trying to keep the barrel nut from galling the receiver threads. VFG can be used, but you should not think of it as grease, but more like a thick oil. Great for use anywhere on the gun, but especially where you do not want your oil to migrate. Example, when you lube your carry gun, the oil will migrate out, and get on your hands, holster, shirt, ect, so you need to wipe it down several time before it stops. Using 0000 VFG, the lube will not tend to migrate, stopping the mess.
Now, where you actually want the oil to migrate, pivot pins, spring wells, ect, then Go Juice works great. Hope that helps a little.
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While you are likely correct, functionally, mechanically this is not sound.
Torque is a very poor way to gauge thread tension. It's akin to gauging air/fuel ratio optimization on a carburetor car just by looking at 1/4 track mile mph and et changes. Yeah, it's kind of meaningful...but not really. We use torque because for most application, strain gauges are not necessary and cost a lot.
This is where K factor comes in. You can apply the same torque to a dry screw as a screw lubed with mineral oil as a screw lubed with an EP type product. The resulting thread tension will be radically different for all. Torque specs need to also specify thread lubrication and type of lube. Most specs assume "light machine oil", but some are speced dry, while still others, are very lube specific.
The milspec barrel nut thread tension was established using torque values for steel on anodized aluminum, lubed with Aeroshell 33 with moly.
While I doubt "it matters", it truly does make a huge difference in actual thread tension/strain, what the parts are lubed with.
The other reason for the lube speced, was galvanic corrosion potential inhibition.