But back to HH for a moment.
So there is all this talk about Robert wanting to see Lyanna, which yeah it's Robert. But when I read the passage from Thrones it's seems rather obvious.
“Robert will never keep to one bed,”
How would Lyanna make this assertion unless she met Robert? We know from thrones Robert had never been in the North before. At the time of Mya, Robert had only been known to be in one bed with one daughter/child. Lyanna' statement suggests she knows Robert gets around, which is true but I doubt at the time of the proposal Ned was like man Lyanna you should see this guy in action.
“Lyanna had told him at Winterfell, on the night long ago when their father had promised her hand to the young Lord of Storm’s End. “I hear he has gotten a child on some girl in the Vale.” Ned had held the babe in his arms; he could scarcely deny her, nor would he lie to his sister, but he had assured her that what Robert did before their betrothal was of no matter, that he was a good man and true who would love her with all his heart. Lyanna had only smiled."
“Love is sweet, dearest Ned, but it cannot change a man’s nature.”
How could she know his nature unless she met him? I am not saying it is out of character for her but we don't really have that established. It's a leap in logic but where does it stem from?
So:
Ned came down from the Vale to HH
All his family is there save Rickard.
At HH Lyanna sees Robert in action, and Robert may have slept with more than one woman there. Not out of character for him.
Now I have seen it speculated that Robert made the proposal after what Rhaegar had done when he crowned Lyanna. Maybe, maybe not.
HH was 10 days.
Howland Reed on the Isle of Faces.
“All that winter the crannogman stayed on the isle, but when the spring broke he heard the wide world calling and knew the time had come to leave.”
I don't know how long the false spring lasted, but this occurs early in the false spring. For that matter I don't know when it began. First moon or 5th moon or what have you. But it is early in the Indian summer.
The tourney had not yet begun.
“A great tourney was about to commence,”
Day 1 HR.
Howland is set upon by 3 squires. Enter the she wold of Winterfell Lyanna.
Howland meets the big bad wolves.
Lyanna cleans up Howland
There is an opening feat that night.
“That evening there was to be a feast in Harrenhal, to mark the opening of the tourney,”
Lyanna drags Howland to the feast
Rhaegar sings Moon River and cries all over his Harp.
Lots of Dancing and drinking
5 Days of Jousting are planned among other things. But it would seem illogical for the Jousting to take place the first five days. More like the last 5 days as after the crowning of the Queen of love and beauty it would pretty much be over. And from Neds recollection I don't think Robert would be all smiles in the melee.
Normally there should be a closing feast, did it happen, if so who said what to Rhaegar or had he left? What did the Starks say to each other? Did the King put an end to it right there?
Anyway is it out of the realm of possibility that the proposal was Neds idea? Ned did not seem thrilled about the loral or perhaps it had already been proposed. Either way we know there was some conflict involved in it. Lyanna did not want Robert and honestly I think she probably liked Robert well enough, just not that kind of like. Robert appears very much like Brandon and I think she probably met and got along with him just fine as she has spent her life around a guy very much like him and it probably would not be a struggle for her to relate to him.
I don't honestly know if Robert would make a proposal, marriage never seemed like his thing and at 18 Robert probably still wanted to have some fun, a lot of fun. Maybe Ned convinced him. It's Ned after all who is trying to convince Lyanna at Winterfell.
So if the proposal does happen at HH it does make perfect sense for Ned to return with Lyanna. Not only to make the offer but to prevent Lyanna from talking her way out of it and to try and convince her that it was going to be ok.
Robert may have gone to the Vale to see Jon. It's not actually mentioned that Robert went to the Tourney with Ned, he may have been coming from Storms End where he is The Lord. So after their father accepts the proposal Ned is trying to rationalize the idea and Lyanna is trying to explain to him the truth about his friend which Ned as we know is often blind too.
Afterwards Ned goes to meet Robert in the Vale and winter returns, leaving Ned and Robert stuck there. Sure they could of traveled but why risk it, it's a second home to them.
There must have also been some interest in the realm during all this. House Stark has become very close with the Tullys, Arryns and Baratheons. While Dorne and the Reach don't get along and nobody seems to care for the Lannisters including the crown. Nobody will marry Tyrion and he seemed hell bent on getting Cersei with the Prince, Tywin refusing every offer for her hand. Tywin is not the type too sit and pout about losses he is a rather proactive fellow.
Tywin played the Aerys self destructive card but without the death of Rhaegar, Elia, the kids, and Lyanna being kidnapped, and Brandon doing what he did, and Aerys calling for the heads of Ned and Robert he is not even close to getting what he wanted. I would think he would have been doing something other than just waiting. Or maybe that's all he did and he lucked into everything else.