The fact that Luke’s hand has fallen into significant disrepair by the end of Star Wars: The Force Awakens, isn’t too shocking.
However, it appears that he never bothered to get the initial damage fixed once he had some downtime following the events of Star Wars: Return of the Jedi.
He’s been off on his own for years and probably hasn’t had much opportunity to get the artificial skin replaced.
Is there some deeper meaning to the fact that he never had this repaired?