Find the transaxle code on the firewall. E58-474 is open diff, most AE92's seem to be fitted with this. E58-11c is LSD and is found on some AE101's. These are the only two codes I know but there are others.
I ended up buying an ae92 halfcut and purchasing the LSD box separately with shafts for $500. The shafts are different between the two so make sure you get LSD shafts with the LSD box.
Kingmick, part numbers for the ae101 e58-11c shafts is:
43420-12391
43410-12392