How could Nunnaly see Lelouch's memories? In the end, when Lelouch is about to die, Nunally holds his hands and is able to see his memories. How? The theory that Lelouch is immortal explains this, but that isn't official.


Is there any official explanation for this?
I am not that sure if there is any official explanation about this. But from what I understand and have answered here,


  Lelouch got his dad's code. He beckoned
  the World of C to lend him its powers, and he took Charles's code
  before Charles passed on. The reason why Lelouch still has his Geass
  is because he didn't take the Code from the same person who gave him
  his Geass: he took his Geass from CC, and he took his Code from
  Charles. Thus, he now possesses both immortality and a Geass. 
  
  To further corroborate this, however, remember that when Nunnally held
  Lelouch's hand he transferred his memories to her. CC also did it when
  Lelouch touched her accidentally back then, so it could be assumed
  that people with Codes are indeliberate telepaths. This leaves us with
  both immortals traversing the world for the rest of eternity.