Okay, a little biology/chemistry lesson here. Urine is normally pH neutral--or there about. It generally ranges from 4-8 on the pH scale with 7 being neutral. Just for some perspective, rain water is usually 5-6 pH. I think baking soda is something like 8 pH. It's been a long time since college

It really isn't the pH of urine that kills the grass, it's the nitrogen in the form of urea.
Think about it, fertilizers have 3 numbers on the bag that correspond to Nitrogen, Phosphate and Potassium. The common source of that nitrogen is--you guessed it--urea. Without having to explain a huge chemical reaction, urea converts to other substances that react with water and oxygen to release large amounts of nitrogen. What happens when you over-fertilize your lawn and end up adding too much nitrogen? You burn it, just like those urine burnt patches! Your best bet is to dilute the urine by watering over the top of it and thereby decreasing the amount of nitrogen that any given area gets.