Board Thread:Lore Discussion/@comment-30529651-20161117203555/@comment-32014963-20170827135551

The Last Dragonborn can be immortal is as likely as the next Archmage who achieved immortality through attaining the necessary level and knowledge of magic or alchemy.

Since the Last Dragonborn is naturally talented in the Thu'um which is a form of magic, I'll say it is entirely possible for him to reach that level of power where he lives on indefinitely because there are those who are born less powerful yet they managed to achieve immortality.

But one thing is for sure. The Last Dragonborn can be immortal but it will not be due to the Dragonborn heritage he was born  with. He can become immortal more easily as he is born far more powerful than the lesser mortals who became immortal nonetheless.