Bringing this back because I actually found from personal experience that you need BOTH LSD axles. The right one (passenger side) has an extra set of smaller splines to engage the LSD, and the left (driver's) side positions the dust sheild/seal about 1/4" outside of where it should be, so you risk oil leaks etc.
Everything I had ever read told me that the left axles were the same for LSD and non-LSD except for a few hints from Keydiver. But, he is right, they aren't the same.