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In this series anything is possible. However in terms of the show I don’t believe Jon lied when he said there was nothing. He was fairly preoccupied with gasping for breath while mentally and emotionally processing he had been stabbed by his NW brothers and was aware that he had died. All this transpires in a matter of seconds so that wouldn’t leave much time, energy or mental strategy for debating over whether or not to lie or tell the truth about what he saw while he was dead. In terms of the books, I believe Jon’s resurrection will play out very differently than the show. In the books I expect Jon wargs into Ghost and would have memories of that. However then he isn’t truly “dead” which could suggest that he doesn’t become darker. Warging doesn’t create the same effect in a person as dying and being resurrected such as Beric Dondarrion & Catelyn Statk indicate.
The problem I see now with Jon’s character if he does warg into Ghost and doesn’t technically die in the books, and doesn’t come back darker, well that’s a huge curveball in terms of what many of us are predicting/expecting as part of Jon’s character development. Or perhaps Jon doesn’t need to die to come back darker and instead being betrayed by his NW brothers is the act that pushes him over the edge and enabled him to release his rage. Psychologically that would be understandable all things considered.