That's a bingo!
Absolutely grease or anti-seize should be used on the barrel nut. I use Aeroshell 33MS and you can also and anti-seize with copper (Loctite CS-A)
The grease and pre-tensioning the nut will give you the proper and true final torque setting. Galvanic corrosion is probably not a real world problem with coated parts (esp hard anodized aluminum), but you ever plan on replacing the barrel a couple years down the line, you are going to be thankful you used something. I've pulled barrels off old guns where I though I was going to snap lugs.
This is all getting into the weeds of how one should put together an AR, but the moral of the story is you have no idea how a used gun was put together.
Someone saying they did it properly is worth exactly 70 inch-pounds of jack-squat at the end of the day.
OP asked how you could mess the process up, turns out there is a long list.
The more "less conventional" the build the more likely you are going to get problems either because you have chosen unwisely in parts selection/combination or put something together backassward.
When the outside of the gun is be-dazzled in decorative-klingon-melee-spikes and the optic is mounted on the handguard, you should pause and ponder what's going on the inside. Not only would I not pay any moneys for this, but you couldn't pay me enough to put my face within 6 feet much less 6 inches of the loaded chamber of that rifle.
Not being ugly, just brutally honest. If my tone is snarky, it's because I open up NES in the morning between my second coffee and first dump.