I have the same problem with my lawn.
I went to Pets Smart recently and came across a product in the vitamins/flea powder etc. section. Unfortunately it is at home and I can't remember the name correctly.........
something like "Green Um" or "Green Lawn" I will have a good look tonite and let you know tomorrow. They come in tablet form and you just have to administer one tablet per day in food or a treat etc. It's supposed to neutralize the acid in the urine, which causes the scortching.........
Now - as for does it work ? well.............
Unfortunately, due to extensive work in my garden recently, I have not been able to try it out yet as my two have been living with my friend Pam (who adores them - it's as though they have gone to a 5 star hotel - and always come back sulking, because I don't allow them to sleep on my bed or watch Neighbours !!) for the last month. Fortunately I get them back on Sunday, and I cannot wait as I am sure you can imagine.
I will try them out next week and keep you all posted, although it might take a while to notice any difference.