While I don't know if I would call the poo ( I guess you can't write poo(p)
) good for the lawn, I don't think that is what is killing the grass. Unless it is being left for a prolonged period of time in hot weather, most of the time it is actually urine that is killing the lawn, by over fertilizing the area. The best thing that you can do is flush the area with plenty of water. Or try to get the dog to go elsewhere. There is also an ole wives tale that female dogs urine is more harmful then a males. This is not really correct since the females usually squat the urine is more concentrated in one area, then if a male were to spray.
If it is not your dog, and you can find the owner, ask him to try to keep his pet on a leash or check with your local laws to see what your rights are.