Can branches of a spruce tree that was peed on & browned come back?

I don't know about the tree, but you can buy a product at nurseries that will discourage the dog. You just have to keep applying it after rains. I did this for a while, then finally told my neighbor to control their dog. They got mad, but it worked. Depending on your neighbor, you might try it.

You can try to remove the dead branch,and apply a small amount of evergreen food in the early morning hrs.

Let it be and let nature take its course, it will be fine. The needles turned brown because the dog peed on it, but it will recover and repair itself. No human intervention required. So sorry about your neighbor, I have one of those too, but he is not that young and should know better . . . Sad part is I know his parents and he wasn't raised that way.

There is a type of spruce, Dwarf Alberta Spruce, that is very slow growing. If your tree is only 3' high after near 20 years, I wonder if it may be that kind. I had one about 12 years that was under 2' but had been nearly a foot tall when I got it. Anyway, that cultivar has a tendency to be plagued by a mite that turns branches brown and often eventually kills the tree. It needs protection from hard winds and piled up snow, but if planted too close to building foundation or a retaining wall, it has higher likelihood of getting the mite infestation. All things I learned later! Trimmiming off brown parts and burning might help reduce infestation vs allowing browned needles drop with larva inside, but my tree struggledseveral years before succumbing despite care. It looked like one might after a dog watered it, but that wasn't the case at my house.

I am inclined to agree with Lydia. There are a lot of things that can cause browning: the kind of soil, drainage, nutrients, and exposure to weather.