Most car manuals (of cars that have LSD's, staggered wheels front ot back, and a space saver), generally say that if one of the rears goes, replace it with one of the front tyres and put the space saver on the front so as to minimise the damage done to the LSD
1. Jack up front.
2. Remove front tire, replace front tire with the space saver.
3. Drop the front down.
4. Jack up the rear.
5. Replace the damaged rear with the front tire removed in step 2.
6. Drop the car down.
7. Limp home.
Sure the fronts are smaller than the rear tires, but they're bigger than the tiny space saver.
Getting back to your original post though, if you went home really slowly, not accelerating hard etc, then I'm guessing your LSD would be ok