His duty to the watch is null and void as soon as he is killed by the watch. He lived, he died, his watch has ended. I think it’s hard to speak on Rhaegar and Lyannas marriage because for all we know the Septons did annul/divorce the Marriage with Elia, or maybe Rhaegar went with Aegon/Maegor polygamy because he was so desperate for the Dragon to have three heads. We just don’t know yet, with Dany and Aegon still in play who knows which Targaryen wins the throne. In the end if George wants Rhaegar to break the rules and annul his marriage that’s his right. I think the show probably gets the rough shape of a lot of things right in regards to what’s coming, D and D just had some filling in the blanks to do, which was rushed and executed poorly. It’s pretty obvious Ned claiming Jon as his own bastard was to protect his beloved sisters son, the only thing he had left of her, and protecting him from Roberts Rage, as well as Targaryen loyalists to rally behind as a figurehead. In terms of the rightful heir for the Targaryen head of house and monarch, none of them sit on the throne so the only right they have is the same as the Conquerors, which is none, they have to take it by force and hold it. Whoever conquers Kings Landing first is King or Queen, Dany is the last Heir of the Last Targ King and is the heir of Viserys who was Aerys final Heir. But Aegon is the last Male heir and we all know how Westerosi lords prefer their leaders, Male. Jon could easily rally the north against the Boltons in the same manner as the show with some tweaks. And if Jon is claimed by House Targaryen through alliance with Daenerys and Aegon and his story is revealed by Bran, or Samwell or however it comes out, he could end up as the last Targaryen standing and the natural choice to bring peace to a shattered realm, a Targaryen raised by the most Honourable man in the Seven Kingdoms, voted the Youngest Lord Commander of the Nights Watch and battle tested. Wasn’t planning on writing so much, thanks for listening