There have been a lot of questions recently, probably due to the warmer dryer weatehr we have been having, about dog's urine burning grass. Many theories are given as to the cause, and food is often mentioned.
Poor food may make matters worse, but even on the best diets like Eden many people still experience some lawn damage, but may be reduced since a diet with high quality proteins is more digestible, so less protein (and therefore nitrogen) is dumped into the urine.
There are many supplements out there claiming to help, but these are unlikely to have any significant benefit. tthey attempt to change the pH of the urine, which isn't the cause of the problem and can leave your pet more prone to urinary stones and infections
Dogs urine has a high concentration of urea, which basically over-fertilises the grass and causes it to die, you often see a ring of strong growth around the dead patch where the concentration became weaker.
It is worse with bitches as they tend to empty the bladder squatted in one place, where boys like to spread it around a bit.
The best ways to reduce the risk are to keep the lawn well watered at all times as this starts the dilution process, and to pour a lot of water over the spot whenever they have emptied to further dilute the urea.