I cannot imagine why it would be seen as immoral for a person on death row to seek comfort from someone else. Even a person who has killed someone else is still a human being with the same desire to be comforted. If we want to bring religion into it, Christian tradition holds that even someone whose sins are "like scarlet" can become "white as snow" if the person is willing to repent. If God is willing to forgive, then why should humans not help a person who is trying to be comforted?
This brings us to one caveat that we should perhaps keep in mind. You could argue that it is immoral to seek comfort under false pretences. Let us say that the person on death row is seeking comfort from a religious person by claiming he wants to "find Jesus." If he says this but does not really mean it, he is lying in an attempt to get more human contact. That is using the other person and is immoral. But if the prisoner is sincere and honest, there is nothing wrong with his attempts to find comfort.