I might as well toss in some info as I'm probably the only guy on this board that has an LSD (and lives in Canada).
I currently work at a Toyota dealership so I was able to get a little more info about the whole topic....
I'm 95% certain that LSD's weren't available in Canada, but that's something I've never been able to find physical proof of (besides the fact that NO ONE has an OEM LSD)...unlike the US where you can buy a rebuild kit, in Canada, the only thing available is a brand new LSD (I think it was around $2600 CAN)
As someone already said, there are a few companies that make aftermarket LSD's for the AE86 and they cost a small fortune especially since we have to deal with the horrible US to Canadian coversion rate.
Now that used OEM LSD's are becoming more and more availble from junkyards in the US, it's the best way to find one for relitively cheap. Don't waste your time looking in Canada because you won't find one. The one problem is that OEM LSD's are based on a clutch type of mechanism and after 15 years many of them won't be very effective...so buying a rebuild kit from the Toyota USA might be the way to fix that.
Also, you must keep in mind that the AE86 changed axle sizes from 85 to the 86/87 models, so an '85 LSD will only work with '85 axles, and in turn, an'86/87 will only work with '86/87 axles.
Nick mentioned that you need LSD axles if you plan on swapping in an OEM LSD and this is true as they are 6-10 mm shorter than the non-LSD units. Though finding LSD axles would be favorable, they seem to be harder to come by than the LSD itself since they're more succeptable to damage (speed + curb = bent axle...as I learned :smile
One alternative is to simply shorten your non LSD axles by cutting off that 6-10mm, which is what I was forced to do.
Hope this helps!
Migs (sliding all over the streets of Calgary)