Is justice always just?

Through Bryan Stevenson's introduction of his book, Just Mercy, we see how Bryan chose the path of a Lawyer and how he fell deeply in love with his work. We learn of a Henry who seems so regretful of whatever crime he did to put him on death row. Bryan humanizes the initial thoughts he had when going to meet a presumably violent inmate and shows how the man is by no means a murderous person and seems "like everyone [he'd] grown up with." Now, is this man deserving of his current situation of living with the fear of death looming overhead with no knowledge of when it is coming? While I don't know the situation of the crime, I think most would assume that Henry, a seemingly sane man with a family to take care of, would not commit a violent crime without reason. Since Henry does not seem like he would commit a crime again and neither does he seem dangerous, would it not be reasonable to say that the purpose of prison has succeeded without the need for any additional time served or capital punishment? So why is Henry still in prison? Is there a need to kill someone for such a long time over one mistake that will never occur again if you leave them alone? I don't know if there is even a solution to this but I do know that the justice system in the United States has many problems.