Dog urine contains high levels of nitrogen, which causes grass to become greener. Under certain conditions (i.e., heat or drought stress) the nitrogen may actually burn the grass, causing it to die and leaving a bare spot in the lawn with a dark green circle around the dead grass. This type of reaction is similar to the damage caused by an over-application of fertilizer. The excess nitrogen in the soil causes the plant to give off moisture, instead of absorbing it, and if the area is not watered thoroughly it may cause the grass plant to die.
This damage can usually be avoided by watering these areas thoroughly to dilute the concentration of nitrogen in the area. If the areas are already dead, they will have to be removed and re-seeded. No home remedy is available, nor will changing your dog’s diet help. A solution that may work for you is to train your dog to eliminate in the same area, such as the back of the yard where it is less noticeable, or in an area with no grass such as a shady spot or a gravel driveway.