I think the closest to the original Manufacturer's recommendation is Castrol Syntrax. They do a formulation for limited slip diffs.
I can't imagine that it's particularly critical, though. I have a Quaife Automatic Torque-Biasing LSD in my car, and when I contacted Quaife to find out the correct oil, they told me that as long as I changed it every couple of years it didn't really matter so long as it's a hypoid oil.
