When I did the 9.25 in my now sold 2011 1500, I used a group 4 based 80w140 that already had the LS additive in there. As test, I added a few oz bottle of GM LS additive. What I found was poorer lockup under load. Unloaded, you could not tell when it engaged but under load with a trailer, the LSD could not lock up.
My second fill with the same fluid, I skipped the extra additive. Unloaded was no discernable difference but it would not engage under heavy load.
So my opinion is don't add any additive. Just add the fluid, put on some miles and see how the engagement is.