The use of gypsum or lime has been advocated in helping prevent dog urine damage. Improved soil quality over time may result in better drainage and less urine concentration at the grass and root level, but it seems unlikely that improved drainage would be obtained with either of these additives. Altering pH, as indicated before, did not affect the spot damage urine can cause.
The use of gypsum will not prevent urine damage. However, it is helpful in neutralizing areas that have had dog-urine burn. This is especially true in the spring. Dogs often like to do their business in places that smell familiar. During the cold winter months this is usually someplace close to the back door. When spring arrives and everything is greening up, you'll probably find a dead spot that refuses to green.
It is here that gypsum can be helpful. It will help neutralize the remaining urine-salts in that area making it possible to successfully re-seed the area. Spread a thin layer of gypsum over the area. Give it a few days to completely neutralize the area before re-seeding.