(Edited for the FAQ: this post now includes the relevant details from the whole thread.)
Limited Slip Differentials were fitted as standard to Chamonix and post-1991 Super Exceed. They might also be fitted to Jasper as standard. Was an option on all trim levels, so you might be lucky.
The factory LSD is a 2-way clutch type with steel plates (rather than friction material), very similar to the Toyota Hilux/Tacoma LSD.
They never fully lock (it's a clutch type, after all), but if they're in good condition with all the clearances in spec they work adequately. Just enough power will lock them up enough to get the van moving, too much power will overcome the clutch friction and allow one wheel to spin. For best results you want to rebuild them and shim the clutch packs so they're at the tight end of the allowable range.
Like the Toyota LSD they can get lazy when they wear. Rebuilding them is relatively easy, and you can make shims that go between the two spring plates to return them to factory clearance.
If LSD was fitted at the factory you'll have an orange sticker on the driver's door, like this:
In English:
(Though the Japanese version says "don't idle" rather than "don't turn", meaning "don't let one wheel turn repeatedly while the other wheel is stationary" because it'll wear out the friction plates really quickly.)
There might also be a LSD filler plug:
If you're still not sure, you can test it mechanically. Lift the rear axle off the ground, handbrake off, and try to turn one wheel forwards. If the other wheel turns forwards then you have an LSD. If the other wheel turns backwards then you have a regular open diff (or an LSD that's completely worn out).
Fluids and quantities are in
the FAQ, but LSX-90 is a bit old fashioned. Modern good quality diff oils are multigrade and LSD compatible (I'd even say to avoid diff oils that aren't LSD compatible, because they're probably inferior quality.) You can use LSD oil in an open or front diff.
I recommend
Redline 75W90 GL-5 in both diffs. It's synthetic and really good quality (My rear diff ran at 70C while towing with decent quality mineral oil, but dropped to 55C with Redline synthetic. Which seems ridiculous.)
Whatever oil you choose, make sure it's GL-5, LSD compatible, and says it's suitable as an SAE80 or SAE90 replacement.
Installing an LSD
The easiest and safest way to install an LSD is to swap out the whole rear axle.
Second easiest is to swap over the complete differential carrier (LSD on left, open on right):
Swapping out the whole carrier/gears/diff assembly means you don't disturb the critical alignment between the ring gear and pinion. You will, however, need to re-shim the axles at the brake end to set the end float as per
the workshop manual.
The trickiest way is to replace only the differential centre. LSD and open diffs use the same carrier, ring and pinion, and bearings so it should be a straight swap, but you need to set the backlash and axle end play correctly. In general if you're swapping the diff centre you don't have to worry about setting the pinion depth, just measure the backlash before you pull your diff apart, and maintain that measurement when you adjust your new diff. That said, this one's best left to a differential/axle shop, but
make sure they have a copy of the workshop manual and follow the specifications: L300 backlash settings are much tighter than your average truck axle.
