Ned's POV:
The sun was beginning to set when he and his cavalry had reached the Reacher lords' camp. The lords of the reach agreed to lift the siege and allowed him to pass to speak with Stannis. Storms' End opened her gates to him and he saw Stannis Baratheon, the lord of Storms' End and Stormlands since Robert's death. Stannis had the same Black hair and Blue eyes as Robert, but where Robert's eyes were full of laughter, Stannis' eyes were hard and full of determination. Which given Stannis' stubborn defiance against the Tyrells, was self-evident. Ned and his honor guard dismounted.
Stannis got the first word in, "Lord Stark, I welcome you Storms' End. Forgive me if I do not offer you bread and salt, we ran out of bread three moons ago".
Ned said, "There is nothing to forgive Lord Stannis. May we speak in your solar"?
Stannis consented to Ned's request, and led Ned to his solar. Once inside, Stannis asked, "It is fortunate that you wished to speak in private as I have some things to discuss with you as well".
Ned was surprised by this, but kept his lordly face that gave nothing away, and replied, "It is certainly fortunate. My lord, I wished to ask if you are planning on pushing your claim like Robert?"
Stannis replied, "I am not my brother, Lord Stark. I am not hungry for glory, wine, or women. It is duty and the rule of law that I desire. I trust you saw the man with bandaged fingers and a bag around his neck"?
Ned replied, "I did".
Stannis continued, "That was Ser Davos Seaworth, formerly Davos of Flea Bottom. A smuggler known throughout the narrow sea. About a week before you arrived he brought a skiff filled to bursting with onions and salt beef. He is the reason why the castle and its garrison were able to hold". Stannis paused and continued, " For his service I knighted him myself and granted him a keep and land in the Rainwoods. Yet for his crimes I took his fingers above the top joint on his choice of hand".
Ned said nothing, letting Stannis make his point.
Stannis said, "Aerys and Rhaegar broke the vows that keep the realm together when Rhaegar took your sister and Aerys murdered your Lord Father and brother. I respect that you took your brother's betrothed as your wife. It's an old and time honored tradition among both the First Men and Andals. Something Aerys and Rhaegar seem to not understand. The kingdoms may have been unified by fire and blood, but it was laws and the duty a vassal owes his liege and the duty a liege owes his vassals that held the kingdom together through civil war, disease, and famine. As Robert's younger brother and heir, I would like to offer myself to wed your sister in his place. In addition, I plan to accept the throne should the lords of the realm consent. I did not conquer the throne nor do I seek it, but if I must take it to ensure order returns to the Seven Kingdoms then I shall take the throne".
Ned was certainly surprised by this, he had meant to ask if Stannis sought the throne the same as Robert, but Stannis had blindsided him with the offer for Lya's hand. He wouldn't ignore her pleas nor would he be like his Lord Father and disregard law and custom to force a marriage alliance.
Ned said, "Lord Stannis I am truly surprised by your offer, but I fear my sister may not feel ready to wed with the events of the war. Perhaps with time and time for her to get to know you, she may feel ready to accept. I must be truthful and say that she held Robert in little regard especially for his appetites. Thus, I believe Lyanna needs to get to know you and choose whether to go through with the betrothal or not".
Stannis replied, "I understand Lord Stark. I do not blame her, and in fact I must admit that I admire her sensible nature. It takes a very intelligent woman to know the flaws that Robert had".
Ned laughed and said, "Sensible is not something I would describe my sister as. She is brave, fierce, and stubborn to a fault. Once she chooses a course, none may gain say her. Though she may be those things, she is also a good judge of character and I think she may find you more suitable than Robert".
Stannis, "I shall take that into account Lord Stark. Now if I may ask, do you have any clue to her whereabouts?"
Ned said, "My men captured Rhaegar's squire at the trident and he has agreed to lead me to her and negotiate a truce with the Kingsguard with her, in exchange for the safety of the Royal family".
Stannis replied, "It appears the Lannisterts' bannermen might have prevented that from falling through".
Ned replied, "The squire was furious at the Lannisters for Prince Aegon's death and the rape and beating of Elia, but alongside Ser Jaime who saved the Princesses, my men are guarding Princess Rhaenys and Elia".
Stannis said, "Lord Tywin would argue it's dangerous to keep them alive, but that is more likely due to his crimes being revealed. Rhaenys being wed to a son of mine with Lyanna would ensure order and stability, but that is an issue for another day. Now, was there anything you wished to ask Lord Stark?"
Ned said, "You covered my question, as it pertained to whether or not you sought the throne, now I must take my leave so I can make final preparations to find my sister and send word of the Great Council to my bannermen".
Stannis replied, "I understand Lord Stark, you have my leave to go and make your preparations along with access to my Rookery".
Ned gave his thanks and took his leave.
Daemon Velayron's POV:
It had been three weeks since Lord Stark entered King's Landing and they had ridden especially hard since Storms' End and separated from the rest of the Northern Cavalry. He had heard that a Lord Rsywell had been given command of the cavalry with the order to reunite with the Northern foot and prepare for a Great Council at Harrenhal. Daemon was unsure what to think about that. It would prevent more war which would honor Prince Rhaegar's wishes as the longer the war lasted, the weaker the realm will be when the time of prophecy would arrive, his prince had told him when they had set out from the Tower of Joy.
As a squire of ten and two, he was not given a full explanation of Prince Rhaegar's plans and visions, but he had overheard him speak to his inner circle and Princess Lyanna about some of the things he saw or had read. Daemon would never claim to be familiar with prophecy and the scrolls of magic and Valyrian prophecy that were in the libraries of Dragonstone and King's Landing. He hadn't even been able to finish the family annals that date back to when they resided in the old Freehold.
He had to admit that Lord Stark's closest companions were not bad company. Theo Wull had an exterior of a hedgehog, but once he opens up he is an honorable and faithful man. Pious by Northern standards and true to his word. He enjoyed his stories about the Northern Mountains and the Wolfswood. Mayhaps he may see it with his own eyes should Princess Lyanna wish her child to see her homeland. Ser Mark Ryswell reminded him of Prince Rhaegar as both men were men of gentle hearts and spoke in a kind manner. Cassel was quick to laugh, but always kept an eye on his surroundings and liege lord. Daemon could tell that this was Lord Stark's captain of the Guard. Lord Howland Reed reminded him of Prince Rhaegar in regards to being clever and knowing things about the world that no one but his prince knew. Daemon wondered if Lord Reed was a man who knew of magic. Perhaps where Prince Rhaegar knew of the magics of Old Valyria and the Red Faith, Lord Reed knew of the magics of the Children of the Forest and First Men. Eathen Glover was the only one who treated him coldly, though he surmised that was because Glover had been with Brandon Stark and imprisoned when Stark had demanded Rhaegar's head.
They arrived at the approach to the tower and he said, "Lord Stark, let me blow the horn, Prince Rhaegar had set a certain pattern to indicate friendly riders or wagons".
Lord Stark said, "Go ahead".
He put the horn to his lips and blew the pattern and tone that Prince Rhaegar had set.
He waited for a return horn blast that would signal to approach.
Soon they heard the return blast that signaled to approach.
Daemon said, "Allow me to lead the approach with the Royal banner".
Lord Stark said, "I will allow it".
He pulled the three headed dragon banner from his saddlebag and tried it to the spear he was carrying. Daemon took the lead and led Lord Stark and his Northern companions to the tower. When they arrived at the tower, he saw Ser Arthur and Ser Gerrold guarding the tower's entrance.
Ser Gerold said, "My lords, if you wish to see her grace I shall need you to disarm".
Theo Wull would have yelled at such a request, but Lord Stark had raised his hand to quiet him. Lord Stark gave an order for them to disarm and dismount.
After that, Ser Gerold led them up the tower to the chamber Rhaegar and Lyanna had shared. Before they had reached the door, they heard a baby cry. It seems like her grace had given birth. When they entered the room, they saw Princess Lyanna sitting on her bed, and in her arms was a nursing babe with his mother's dark brown hair. When her Grace heard Ser Gerold beg forgiveness for the intrusion and announce their arrival.
Ned's POV:
Lyanna said, "Ned, I am so happy to see you. Come meet your new nephew," she paused and then continued, "Ah you just missed Ashara and little Alyssa. Our niece needed to be put to bed".
He was visibly shocked, but soon a smile took hold on his face, and said as he made his way to the bed, "Oh Lya".
When he arrived at the bed he took a moment to gather his words and he felt his cold and solemn lordly face melt before seeing his Lya and her son. Ned soon spoke, "What's his name, Lya"?
Lya replied, "Jaehaerys, Rhaegar was certain our child would be a girl so he had wanted Visenya, but I was stubborn in believing the babe would be a boy. Would you believe that it took us a fortnight to decide on a name if the babe was a boy, Ned? I wanted Jon after the King in the North who drove the pirates out of the White Knife and raised the Wolf's Den to guard the people of the North. Rhaegar had liked that name since boy or girl our child is destined to protect the realm.."
He asked, "Lya, what are you talking about? What destiny"?
Lya's face turned into an expression that Ned had seen so many times when they had been children, a pout of annoyance. She said, "Let me finish Ned, and I will tell you," continuing, "So Rhaegar liked it because it spoke of our child's destiny to protect the realm from the Second Long Night and the Others. Rhaegar reminded me that our child needed a regnal name of Valyrian origins, especially for our firstborn, thus we agreed on Jaehaerys after the Conciliator and Rhaegar's grandfather. He said it would go better with the lords and the faith in case people took offense to the second marriage, even though no law had ever been established against his house in that matter.". She paused and said, "I guess he bears another trait of his namesake, his father was murdered and it is up to his mother to guide and protect him to the Kingship".
Ned said, "Daemon gave me some information that prophecy was involved but he didn't know much in detail nor how everyone came to believe that you were kidnapped".
Lya saighed and then explained the events that led up to her elopement and pregnancy.
He just stood there in shock and surprise when Lya had finished.
The Rebellion had been based on lies and that Lyanna and Rhaegar ran away together for her to be free from Robert, a love that seemed more fitting for a song than real life, and out of prophecy that seemed like madness. And included a betrayal that they had not expected.
Author's Notes: While I use this to explain my story, I would prefer to discuss these questions in private. If my writing seemed biased it's because I am trying to emulate Martin's style of writing, with fallible and biased POV characters as all people have their own preconceived notions and are imperfect by the very nature of being human. For example Jaime was never a religious person which is why I wrote in a more cynical tone when mentioning the new gods in his POV.
Martin follows more pop history than true history, medieval women had far more rights than is believed by modern people. The Catholic Church numerous times stressed the requirement that marriage vows were only valid if both the groom and bride made the vows of their own free will and free from coercion. Funnily enough Martin even mentions that vows made at swordpoint are not valid when Cersei forces Sansa to marry Tyrion. So Lyanna had the right to refuse the match and her own refusal would carry more weight if her brothers agreed with her, especially the one who knew Robert.
According to the wiki, Robert declared himself King and A World of Ice and Fire makes no mention of who makes the declaration. In addition, given Robert's bloodlust it makes more sense for him to crown himself given how the rebels didn't take up the position to depose Aerys and place infant Aegon on the throne with their own men controlling the regency. He also had one confirmed bastard and fathered another during the Battle of the Bells, it is not out of character to have him have more at the time.