I have dogs... not every bladder event is going to make a brown spot... its basically nitrogen overload. It was usually the longer pees after holding it for a while that might cause damage.

I try not to let my dogs eliminate on other people's yards, though sometimes it is impossible to prevent. We have a fenced in back yard and my dogs have been trained to do their business there, before we go on a walk. Even though we do that, sometimes it still happens while we are walking... its instinctive for them to mark.

If its becomes a problem - ask your neighbor to train their dogs to go in a particular location that is not on your property.

I live on a large lot now so I don't do this anymore... but when we had a small yard, we had a mulched patch behind a fence screen where my dogs were trained to go. The mulch is generally going to absorb the urine and the odor and its easy to pick up the piles from... and I would add a fresh layer of mulch about twice a year. It kept things neat and hidden. You could encourage your neighbor do something like that....

and when all else fails, I have sprinkled sugar - which is pure carbon - on the areas that seemed to be getting hit the most and then watered it in. dilution is the solution. The carbon offsets the Nitrogen... similar to the way wood chip mulch does...

I agree with what joebyeweed said. If your soil is lacking in microbes or otherwise unhealthy, then any dog can cause spots. If your soil is healthy, then no dog will cause the spots. A handful of table sugar should cure your spots until you can get your soil more healthy (hint: use organic fertilizer at least once per year).

I have always fertilized my lawn it looks healthy. But I have never used organic fertilizer. Al;ways wanted those chemicals to give me that green effect. Would organic make a difference in brown spots as well as that nice green healthy look??

Here's a sample of what alfalfa pellets (rabbit food) can do. Alfalfa is a common ingredient in organic fertilizer.

{{gwi:79339}}

Note the improved color, density, and growth. The picture was taken one month after using the alfalfa.

Using the organic at least once a year should keep enough biology alive in the soil for the dog pee to not harm the grass. You can use it any time whether you just used chemicals or not.