Sadly, there's not much you can do except flush the area thoroughly with water after every urination. This burning is going to happen when you have a dog that can run at will in the backyard. You could create a small, fenced-in corner of the yard where you can place the puppy every time it needs to go. That and walking the dog instead of letting it run in the backyard would help. Adding lime to the spots would be unhelpful. A common misperception is that the spots occur because dog urine is acidic. In truth, the spots happen because the urine is full of salts-and that's why flushing with water helps; the water dilutes the salts to levels that will not harm your lawn.