Lucas oil treatment
Lucas does great chemical engineering, and their products are uniformly good stuff. And, yes, that's the product in the plastic display case with the little gears. I'm not familiar with the other products mentioned, maybe they're as good or better, I don't know.
The real advantage of the stuff in a differential is that it improves the viscosity of the oil at high temperatures and keeps the oil seals from getting brittle. The differential does get hot, and you don't want your oil getting too runny. And I really hate to have to take the whole thing apart to replace a pinion oil seal.
It's supposed to have an effect on the cushioning ability of the oil, to keep one gear from actually crashing against the other as they spin, at, like, a molecular level. But I think that's what hypoid oil does anyway.
In a conventional limited slip differential (as opposed to locking or Eaton Tru-Trac) that uses clutches to moderate the torque, the Lucas stuff is supposed to be able to replace the friction modifier you're supposed to add to the hypoid oil.
It says on the bottle to use from 50% to 100% Lucas stuff in differentials, but that seems a bit extreme to me. It's like the medicines that say "take two" when one will do, or laundry detergent that says "use one full cup" when a quarter cup will do. They clearly want to sell more product.
I'm in the process of rebuilding both front and rear differentials (w/Eaton Tru-Trac's) on my '90 GMC 1500 'Burb (the stock rear 10-bolt carrier busted and I want to change the ratios anyway), and I plan to put about 25% Lucas oil goo in them.
=====
To Hell with the shame, fear, and guilt thing. I'm not doing that anymore. I'm doing love. Especially for the arse-wholes. Lord knows they need it!