Warning: I am primarily a fan of the show, not the books. I don't really care who Azor Ahai is. All I can tell you is that I wanted to give the characters in this show a happy ending before it all goes to hell in canon.
Spoilers for 8 x 03 and speculation far beyond that, including a persistent rumor about events in the finale.
In the end, it was decided that the best way to resolve the battle for the Iron Throne was to dissolve it completely.
It had been a savage war, far more savage than any of its players had fought up to this point. Euron and Cersei were dead. Most of King's Landing was in ruins. The last battle had imploded in an unholy conflagration of wildfire, much as it had several months before, and when it was all over there was a villain and a hero to enchant further generations with songs of their own making. One had emerged mortal, the other not so much, neither of them expecting to survive until the end: a Targaryen who wanted nothing more than to walk away from the title and a Lannister who had betrayed his own family in order to bring an end to this sad, sorry, bloody tale.
Neither Jon or Tyrion had any desire to continue playing their unchosen roles in this morality play. And they didn't.
Jon and Dany granted Tyrion the most generous of pardons: he was exiled from King's Landing and allowed to go home to Winterfell. Sansa and Tyrion had dispensed with the formalities and decided to consider themselves married. Sansa didn't accept him out of pity, nor did Tyrion retreat to Winterfell in penance for his role in the war. They had forged an understanding since that night in the crypts: their marriage might not have come into being as a result of passion or freedom, but there had been a friendship and a kindness established at the very beginning, and neither of them had forgotten that in everything that had happened since. They had been outcasts placed into roles of influence out of circumstance who had subsequently both suffered and done horrible things as a result of that suffering. The wisdom that came out of that had been hard fought, and if Sansa's judgment had been tempered by the decisions that she hadn't had to make, then perhaps that was a lesson well learned for a successful partnership.
They weren't madly in love, but her parents had not been, either. They cared for each other and wanted to rule justly for the people in their charge. That was the life that both of them wanted, and they could easily see it in each other.
The passion came quickly enough. Twelve months after Tyrion had come back to Winterfell, Sansa gave birth to their son. He was the first of their many frighteningly erudite children. The Seven Kingdoms might not have been destined to be ruled by a just woman and an honorable man, but the North certainly was.
Jon himself had no taste or talent for kingship. Nor did he desire to rule by Dany's side, balancing out the crueler of her impulses and spending the rest of his existence keeping multiple threats at bay. He wasn't even certain if his existence had an end point: if it didn't, he certainly wasn't going to spend the rest of it here, tortured by the claims of yet another responsibility he didn't want. He had helped bring about the end of the war and he had influenced Dany to give the Seven Kingdoms their independence. Beyond that, he knew that the crown belonged to her. She had done far more to earn it than he ever had. The decision to hand the crown over to her had been an easy one.
Dany maintained the institution of the Kingsguard, but decreed that its members no longer had to serve a lifetime appointment and were allowed to marry. Jaime and Brienne were the first to take advantage of this new freedom, agreeing to serve a term of seven years before retiring to Tarth. Misanndei and Grey Worm returned from Narth just in time for Misanndei to rejoin Dany's side as one of her most trusted advisors while Grey Worm signed into service beside the newly wedded knights. Daario wrote Dany and pledged his service to her, but Dany declined: he was needed in Essos, and she was needed here.
The rest of the combatants in the war scattered to different corners of the realm. Bran retreated to Winterfell and was absorbed into the Godswood. Davos agreed to stay on as the Hand of the Queen, but he retired to Winterfell after just a few years, finding the surrogate grandchildren in Sansa and Tyrion's children that he had been denied in life. Arya and Gendry signed on to remain unofficially in Dany's employ with the unspoken understanding that Jon would not ask too many questions about the exact terms of their services. Bronn was granted a castle in the westerlands in return for informing Dany of Cersei's offer to slay the Lannister brothers. Edmure Tully was allowed to return to his home in the riverlands with his wife and son. Yara returned to the Iron Islands to rule her people as the last living Greyjoy. Tormund and The Hound departed for the pockets of free folk that had scraped out an existence around the remnants of the Wall, armed with stories of the defeat of the Mountain at his brother's hand and the Hound's ill-tempered grunts every time Tormund tried to embellish the tale.
More than a year after they had established a ramshackle community there, the former king came to join them.
He was not alone.
Dany had spent many of the months preparing toward war secluded from her armies at Winterfell for undisclosed reasons while Jon remained by her side. The real reason for her absence wasn't known to most of her supporters, but the Starks were well aware of the secrets contained within the castle walls, hidden from most of the world's knowledge until Dany could safely take the throne.
They were brown-eyed and inseparable, one blessed with her father's raven hair, the other with her mother's golden tresses.
Dany named them Lyanna and Jora, after the fallen soldiers of House Mormont.
Jon had spent most of the months leading up to their birth not focused on intrigue or danger or war, but troubled by the twisted bloodline that he had helped bring into being. He and Dany had married early in her pregnancy in order to assure legitimacy, but Jon never felt right about it: what if the sickness that had taken root in their grandfather was repeated a second time in their child? Would it be another Mad King, another Joffrey Baratheon, seemingly destined to foist misery and death upon the world? What if its older brother had not been felled by magic as Dany believed, but had simply perished because that mingled bloodline was destined to end in sickness and ruin?
Tyrion had reassured him that blood wasn't necessarily destiny, that Joffrey's mind had been twisted but that of his younger brother and sister had not. Jon didn't know who to trust or believe about any of it. Dany didn't understand why he was so afraid: she, after all, had been raised to believe that this same twisted bloodline was a sign of purity, a divine ordinance that guaranteed her birthright.
Jon still loved her, but he knew by then that they were a bad match.
The girls were born healthy and clear-eyed, and the moment that Jon held them he knew that they were his. Jora looked at him solemnly, as if she understood the deeper part of him: Lyanna's eyes pierced into his, looked around fretfully, and then opened her mouth and wailed. He knew then that they were twin reflections of Dany and himself, and his destiny lay not in armies or empires, but in the family he had now created.
Once a semblance of peace and order had returned to the stormlands, the decision was made. Dany had named the girls, but Jon would be the one to raise them.
"You're divinely protected," Dany told him. "I'm not. It's your job to protect them. If either of them wants to learn to rule after me when the time comes, they can. But they deserve a childhood first."
Jon couldn't argue. He had never wanted to be a king: the only thing that any sort of authority had given him was a death that he couldn't keep. Dany's drive, her passion, her many years of struggle and sacrifice had been leading towards the kingdom that she had chosen by will as well as by blood. He didn't belong there.
Jon ventured with Ghost and his daughters up to the fledgling village that Tormund and the Hound called home. Sam had moved there with his growing family in the past year: what he lacked in survival skills Gilly was proud to teach him, and he was writing a chronicle of their adventures in his spare time. Jon taught the girls to hunt and fish, and they quickly adapted to wildling life. Lyanna was a born adventurer, as feisty and headstrong as the mother that she resembled, fiercely dedicated to the life that they lived. Jora was quieter, more reticent, and distinctly more intellectual: Jon planned on sending her to Winterfell to learn the realities of being a queen when she came of age. If she took well to it, he'd send her to her mother, to learn the art of being a true ruler.
If she wanted it, that is. Jon knew only too well the misery of being forced into that role against your will.
He and Dany exchanged letters a few times a year. The stormlands were thriving and productive. Kings Landing had been rebuilt. Her dragons were staying out of trouble.
She was happy.
And for the first time in his life, Jon knew that he was, too.
He had grown up an outcast on the outskirts of a family that he had desired: loved and protected by some members of his family and resented by others. He knew now that he had been placed in that situation out of love: Ned had cherished and protected him as his own son in the only way that was possible, and it was his memories of that family that Jon most sought to emulate. He hadn't wanted to father another child to be raised in the same circumstances, but he had understood too late how close he had gotten to what he had wanted. If blood had been destiny for him the same way it had been for Dany, he would have chased the same destiny she had, of adventure and intrigue and power. The blood that ran in his veins may have been Rhaegar and Lyanna's, but he didn't understand them. Not at all.
He had wanted a real home, a community, to be accepted. To belong. He had wanted not to be displaced, not to have to cling to titles that didn't belong to him. Rhaegar was a distant figure, a ghost: what he had most wanted to become was Ned, who had put roots deep down in the soil and raised his many children to be as honorable as he was.
The wars were fought. The songs had been sung. He had helped save the world. Twice. Now it was time for calm, a dream of spring forged in the depths of winter.
He was home. He planned to stay there for a long time.