I am not sure if the immortality legend was something that was added during the Arthurian Legend or not.
From another post I remembered writing:
Originally Posted by Smitty
The Grail was a creation of Chrétien de Troyes in his 12th century Perceval, le Conte du Graal. It was distinct from the chalice of the Last Supper, and it was from this salver that a wealth of Arthurian romances grew. The Last Crusade is a continuation of that questing tradition, by merging the myth of the cup Jesus supposedly drank from with the different cup that supposedly caught his blood on cross.