hmm, by description .. yup
lsd will run as you say, with both outputs in same direction..
how much did u give ?
also a slipper isnt that easy to turn over by hand, as you have an internal clutch to fight against.
best to get it on car mounted, and give the wheels a spin.
the weight of the wheels should sort the clutch out and show you what it is.
also the code on the diff (small metal dog-tag lookin mofo) will tell you type and ratio of the diff.
its normally located on or around one of the drain plugs iirc