Im not too sure how the dealer would be able to tell you that by looking at the vin, since no E39 came with the LSD except M5.
Now if your friend knows what he's talking about then the previous owner swapped it in.
If you wanna be 100% sure what fluids you should be using, i would strongly recommend you call the transmission experts such at "Toronto Automatic Transmission" and ask them. They rebuild transmissions and differencials for the dealerships.
Ask for Bob or Mathew, they know what they are doing.