John brings Lee's body out to rest by a tree, to determine where to bury the boy. It's one of the few scenes in all of Yellowstone where we see John give into the overwhelming grief that defines his life. In the midst of his sadness, John sees a goldfinch land on the ground. He takes that image in and acknowledges it as a sign that he should bury Lee right there. There's never explicit mention of this, however, so you might miss the great relevance of this small animal.
Despite the fact that this is a story about people, nature is utterly central to it. The beautiful mountains, forests, and fields of Montana surround the characters, while the bears, wolves, elk, bison cattle, and horses stride alongside them. It makes sense, then, that John lets a pretty little bird determine where he buries his beloved eldest son. Of all his children, Lee had the closest connection to the animals around him. In many ways, Lee was John's favorite because he was the simplest child. It's only right to honor him in such a powerfully simple way.