Here's a wild guess:
If you jack-up one rear wheel, then switch of TC, put in gear and rev the engine - if no LSD, the wheel on the jack should turn freely while the other is firmly on the ground. 
On the other hand, if you have LSD, then wheel on the ground will also start rotating (albeit at a much lower speed then the jacked-up wheel) and er... the car will fall of the Jack and fly forward... or something... so maybe not such a good idea... 
So perhaps not a very practical test but as a matter of principal I think this would prove LSD / no-LSD? 
LMAO!
I think I'll stick to trying the steering lock and dumping the clutch test first. Maybe I'll try your way if I'm still not sure......

but if you dont have an LSD you can always do this 
I'm sure that pic means something to some people, but to me it's just some bits of metal....

A safe way to do the above test might be to park up with one wheel on an area of low traction, a grass verge by the side of the road, for example, while the other wheel is on tarmac, switch off the TC and pull away swiftly.
And if I leave a wheelspin mark in the grass then I don't have a LSD right?