I used Mobil 1 75-90w full synthetic. It took about 1.5 qt.

Since we don't have a factory LSD, I cant see why they say you need an additive. However, it DOES need to be a Hypoid oil (Hi/Extreme-Pressure). That Castrol looks like it would fit the bill...

FWIW, The recommended fluids (Specs) are listed in the manual.

Disclaimer: I am not a certified mechanic, I just play one on tv... so, take my advise with a grain of salt.