As I said before, if it's a viscous LSD which you have unless you've taken a mechanical diff off a GTR or put an aftermarket LSD in, the LSD part on a viscous diff is sealed. LSD oil won't hurt it but it is $100 down the drain though.
As for oil, check for alternatives in the "Goods on oils" sticky in this forum because $80 will buy you a *proper* synthetic oil at supercheap if that's the only local store near you. Examples are GW syn-x 6000, royal purple HPR, castrol edge, motul 8100 x-cess/x-max, penrite racing 10 tenths etc. Motul 4100 while great, is still but a semi-synth, $90 + filter is just too much for it.