Thank you! It’s getting more action now than ever. It appears I’ve seriously underestimated fandom’s fondness of AUs though, especially ones involving genderbend. And as I have a tendency to fall down the rabbit hole with any gives AU, my answers tend to get a tad lengthy.

Anyways, fostering, betrothals and a rebellion under the cut.

First thing that would change if Ned is a girl is his fostering in the Vale: being a girl, Eddara would not get fostered in the Vale with Jon Arryn since Westerosi girls typically only get fostered as a part of a betrothal agreement, or a hostage situation so that changes the relationships between the characters from the get go. Politically, Rickard Stark’s “southron ambitions” mean that he’d still be keen on a fostering happening, and that leaves the Lord of Winterfell with Brandon and Benjen to use as an instrument for alliance via fostering. On the surface, Brandon might be an obvious choice as his age would make him a natural companion to Robert (and presumably, Elbert Arryn) which makes for a neat and strong personal alliance between the three future rulers, but it seems that Rickard was cognizant IOTL of the importance of fostering his heir in the North so that Brandon could get to know the land he would rule someday and establish relationships with his future bannermen. Certainly, with the Northners’ innate wariness of southron influence and culture, Rickard, already of a mind to betroth his heir to the south as a part of a multi-kingdom alliance, might figure that having that same heir fostered in the south–particularly in the Vale, the historical center of Andal invasion and culture–would be too provoking for his bannermen and might lead to Brandon being viewed as too southron and an almost stranger to the people he would rule over. A second son would be a much less aggravating choice in that context and limit the chances of the Northern lords growing disgruntled by the rule of a southron-leaning Winterfell. Now, note that Benjen would be too young to be sent to the Vale at the same date as canon!Ned (Ned was fostered at 8 so Ben would be 3 if not younger), but there is no reason for Rickard not to send him to be a page once he hits the appropriate age. A slight complication might present itself in the (at least) six years age gap between Ben and Robert which might not initially allow for the easy camaraderie Robert and Ned enjoyed IOTL, but with Jon Arryn encouraging a relationship between the two, and perhaps even setting Ben to squire for Robert at tourneys and such, they can still build a personal relationship to be a cornerstone of the Stark-Baratheon alliance.

Next up, the SA betrothals. I do not know if Robert’s relationship with Ben would necessarily lead him to propose the match to Lyanna the way his friendship with Ned did (that is if Ben is fostered in the Vale, and Rickard does not pull a Hoster Tully and opt for just marriage alliances.) If there is no Ned to grow up with Robert as his chosen brother or to
talk about his beloved siblings and likeable family or to show Robert
the close familial bond the Starks share, would Robert still propose the
betrothal to Lyanna?

I imagine that Jon Arryn would certainly encourage Robert to make a
match within the slowly-forming Southron Ambitions bloc, and while Lysa
Tully is also an advantageous option for the young Lord of Storm’s End
that would serve the bloc’s interests just as well, Hoster Tully
evidently had his eyes on a match with Jaime Lannister, though we do not
know how far back he had that match in mind. Perhaps,
as Jon Arryn might figure, it would be a better idea to direct Robert to
the Starks and leave Lysa free for the planned betrothal with Jaime
that gives the bloc an additional strategic, economic and military
advantage.

Certainly, the match between Robert and a Stark would also seem like a
natural choice if young Ben is indeed squiring in the Vale which makes
Robert’s existing relationship with him a good stepping stone for a
betrothal to reaffirm the Stark-Baratheon relationship.

The main question here, however, is which Stark daughter the match would be for. I do not believe that Robert’s “love” for Lyanna was because of her personality or beauty or anything to do with her, as much as it was about his desire to be Ned’s brother, so there is nothing in particular that would point to Lyanna specifically. Eddara, as the eldest, might seem like an obvious choice, perhaps preferable for Rickard as well since her age in 279 – the earliest possible date for the Robert-Lyanna betrothal IOTL – could allow a marriage to happen much sooner than Lyanna whose age necessitated for the marriage to wait a couple of years if Rickard did not wish to jeopardize her ability to produce children to support the generational alliance planned for years between the kingdoms. On the other hand, would Eddara even be unpromised in 279? She’d be 16, hardly an ancient age for a Westerosi maiden to be unbetrothed but still atypical, especially if we consider that Rickard betrothed Brandon at 14 and Lyanna at 12 IOTL. I’m not discounting that possibility that she might though: Rickard, clearly ambitious for his children’s marriage prospective and keen to use their hands to reaffirm his alliances, would wait for the most advantageous match for his eldest daughter (he would not be the first Lord Paramount to do so: look at Tywin keeping Cersei’s hand free after the rejection from Aerys, or Mace Tyrell dangling Willas’ hand) so with two eligible bachelors among the bloc’s conspirators, he’d probably keep his daughters’ hands free to score the greatest possible match.

But this is where the unknown variable of Elbert Arryn factors in.
We have no knowledge of what Jon Arryn’s marital plans for his nephew
were, how old Elbert was, or if he was betrothed when he died IOTL or not. It’s definitely weird that we do not hear about Elbert being involved in the SA’s betrothals since Jon Arryn had no horse in the marital race, and Elbert was the heir to the Eyrie and to a line hard-pressed for male heirs in the main line. Was that because there was no bride to match with him IOTL with Catelyn, Lyanna and (supposedly) Lysa being spoken for? Did Jon Arryn simply have his eyes on a grander match for his nephew, Cersei perhaps? It’s hard to say for sure but for the purpose of this ask, one has to wonder: wouldn’t he be an obvious match for one of the Stark daughters? A Stark-Arryn match would nicely reaffirm the alliance between the two Great Houses and create a neat web of intra-bloc marriages while still leaving one Stark daughter available for a betrothal to Robert (which was perhaps the most important betrothal in the bloc since Robert’s closeness to the throne made him a cross between an insurance policy, and a proverbial knife that could be held to the main Targaryen line’s throat) That marital design would certainly appeal to the ambitious Rickard Stark as it gives him ties to three Lords Paramount, and a future in which his grandchildren would rule the North, the Vale and the Stormlands with kin ruling the Riverlands. It’s quite the fruitful design, and while it might be pushing the Northern bannermen a bit too much imho, Rickard might figure it is worth it. After all, he’d still have Benjen to marry to the North to smooth any ruffled feathers from his disgruntled vassals, and the Northern-raised Brandon would certainly be encouraged to capitalize on the connections he made during his own fostering at Barrowton.

The difficulty here is that we don’t know how old Elbert was or if Jon Arryn would seek to betroth him before 279. Perhaps he’d prefer to keep Elbert unbetrothed to seek the most advantageous possible match, or Robert would propose the match with the Starks first, or Rickard would not consent to marrying both daughters to the south. Bottom line, we might be looking at an Elbert-Eddara and a Robert-Lyanna match, or Robert-Eddara and Elbert-Lyanna, or Robert-Eddara and Lyanna-Nothern son if Rickard decides that fostering his “spare” and betrothing his three other children to the south could lead to unwanted discord in the North.

Regardless of how the betrothals go, I do not believe they would alter the events of Harrenhal:
it does not matter whether Lyanna was betrothed to Robert, to Elbert,
to a Northerner or even unbetrothed; she’d still defend Howland’s
honor as the Knight of the Laughing Tree and almost certainly get
discovered by Rhaegar leading to her crowning. While a betrothal to
Robert or Elbert would mean that Rhaegar’s actions poses an insult to
two Great Houses instead of one and jeopardizes the marital alliance, the insult to House Stark and Lyanna’s
honor alone would still reverberate within the entire bloc. Similarly, I do not think the identity of her betrothed would change the outcome of Lyanna meeting with Rhaegar, namely her disappearance with him. Even if Lyanna was not driven by her desire to avoid a marriage to Robert, or if she wanted to refuse Rhaegar, I sincerely doubt that Rhaegar would take no for an answer. He was set on having the third head of the dragon from Lyanna, and he was not going to politely turn around and go back to Dragonstone or simply find another woman to impregnate if Lyanna refused him. I can not stress enough how utterly vulnerable Lyanna was in that situation, alone and faced by the crown prince and two Kingsguard sworn to protect him – and easily capable of simply forcing her if she’d said no. Ultimately, I do not think Lyanna giving or withholding consent would have changed the outcome of her being whisked away to Dorne and Brandon riding to his death in King’s Landing. The only thing that I can see changing the outcome of that is if Lyanna’s location changes in this au for whatever reason but I’d be getting too ficcy if I tackle that.

From there on out, some things would remain the same, and some would be unknown. The rebellion is inevitable once Aerys executes the two Starks, Royces, Mallisters, and Elbert Arryn. Ben’s age and status as the last surviving male Stark means he’d surely be counseled not to take the field himself lest he dies and House Stark dwindles to Eddara, though whether he’d heed that counsel or insist on riding to war himself is speculative. The marriage to Catelyn would definitely still happen because Hoster Tully is not giving up on making his daughter the Lady of Winterfell, but I wonder about the Jon ArrynLysa match. If Elbert was matched with Eddara, they might get married and perhaps even conceive prior to his death. Honestly, where would Eddara even be at the time? Winterfell? Riverrun? The Vale? Is she married? Was she on her way to be married at Riverrun in a double wedding? Was she left behind as the Stark in Winterfell? Was she with Lyanna when Rhaegar fell upon them? Who the hell knows. But one place she wouldn’t be is the field. Which raises the question of what would happen when the information about Lyanna being in Dorne arrives.

No, scratch that, would the information even arrive in time? Would it arrive at all? Because even if Ben is indeed on the field, he would not be the one given the command to proceed from the Trident to King’s Landing, or to lift the siege of Storm’s End. We don’t even know when or how Ned received that info IOTL, but we do know that he stormed out of King’s Landing the same day of Robert’s arrival after fighting with him over the murder of Princess Elia and her children, and he arrived only a short time before Lyanna died. A single day could end up making a lot of difference in what happens next. And if we assume that the timing of everything was precise and Ben does receive the information in time, would he proceed like Ned and make for Dorne with only that small band of companions or have a little more men? Would he survive the fight with the Kingsguard? Would others besides Howland?
Would Ben have the same reaction as Ned and claim Jon as his own bastard? Would he bring him to Winterfell or entrusts him to Howland? It’s impossible to say so I’ll leave that one to fic writers.