Shame and suffering
It was a few days after Jamie was banished to the Nights Watch that Eddard was able to talk with Lyanna in private. The Lord of Winterfell found his sister in the Godswood of the Red Keep, praying to her ancestral Gods and incidentally kneeling in the same place where Robert prayed for her deliverance.
This is as safe a place as any to talk in privacy. There are no hiding places for anyone hopping to listen in.
Lyanna notices her older bother when he kneels front of the heart tree next to her.
"While you were under, Robert prayed for your recovery. When I arrived in the city I found him kneeling in that very spot. He has been by your side during your whole coma, refusing to leave for any reason."
When Eddard saw how sad Lyanna looked, he worried she did not believe him. He took her hands in his so that she knew he was telling the truth.
"Robert really does love you with all his heart."
If anything, this seemed to make Lyanna even more sad. However, she wasted no time explaining why she was sad.
"I don't see how Robert could love me now, not after what ... after what happened."
There was a pause. Neither of them had any doubt as to what was meant by this.
Eddard was the first one to break the silence. "Robert loves you very much, and so do Benjan and I. Nothing in the world could possibly change that."
It seemed Lyanna did not hear this. She just continued, almost as though she was talking to herself. Her voice was hollow, drained of all ethos. It was as the emotion of the ordeal was being blocked.
"At the tourney, after he gave me the crown, the Prince asked me to visit him in his tent. When I got there, he told me he wanted me to run away with him and be his paramour. I refused him, told him I was betrothed to another, that I could not turn my back on my family. He just smiled, poured me some wine, and asked we at least toast 'to destiny'. When whatever he put in my cup wore off, I was in the tower in the room where you found me."
This is what Lyanna told her brother. She did not need to tell him all the details. Lyanna did not tell her brother how Prince Rhaegar took her while she was out cold. Nor did Lyanna talk about how she shosted and screamed curses and made sure the prince knew that she knew what he did. Lyanna never brought up how Prince Rhaegar kept repeating that "it is for the good of the world" and how "you are my Queen of Love and Beauty", or how he put sweetsleep in her food whenever he wanted to take her.
Lyanna was shaken by this ordeal, even the memory burned like a nightmare from which there was no waking up. The She-Wolf got out of kneeling position and curled up in a bowl. Eddard's heart was strained by what he had just heard, even though he already suspected this when he found her.
Placing a hand on Lyanna's shoulder, Eddard looked his sister in the eyes. "You have to believe me, this is not your fault. He had no right to do what he did, and what he did was wrong. I promise you, we all still love you very much and nothing could possibly change that."
Lyanna heard this. She truly appreciated how much better her life was for the family she had. However, she still was afraid.
"You still made a promise."
"Don't worry, I intend to keep my word. If for no other reason than because I love you."
Lyanna breathed a sigh of relief. Her brother continued.
"Come now, I have someone I would like you to meet."
After walking through the hallways of the Red Keep, Eddard and his sister were in the nursery.
Formerly the Royal Nursery, this is where Selwyn Tarth stood between Elia Martell and Gregor Clegane so as to prevent the latter from harming the former. However, this room has long since been cleaned up. Any symbols of the old regime have been removed, and are in the process of being removed. Even the dragon skulls that hung from the throne room are being taken down and moved to the wine cellar.
Next to the window was a peasant woman, nursing a small black haired babe.
Lyanna could not stop staring at the baby.
"Sister, I would like you to meet your nephew: Jon Snow."
Wylla handed Eddard the baby, and Eddard Stark rocked it gently in his arms to soothe its crying.
Lyanna cried, but while she cried she actually smiled. The baby looked like Eddard, and if Jon is raised in Winterfell he will probably take after Eddard. Or Brandon. Or Rickard.
What matters is that Jon Snow will be raised with love, and will never become a Rhaegar.
Lyanna doesn't remember Eddard offering her the baby, but he must have as she soon found it in her arms. She gently rocked the baby back and forth until it was once again asleep.