Hi! I have read the theory that Lady Stoneheart's (LS) endgame is tied with Arya. However, I wonder how this impacts Jaime's arc, inasmuch as his has changed throughout ASOIAF. I think the Valonquar=Jaime theory is strong too. But Brienne's arc also has association with Jaime's. Is GRRM really going to build up Jaime until he murders Cersei, and then immediately knock him out of the story? How do you think GRRM going to trace Jaime's path between LS and Cersei, if and when either is to happen?
Jaime and Brienne will get away from Stoneheart and the Brotherhood somehow; possibly through interference by Thoros or the Brotherhood splinter group (Edric Dayne et al), possibly through something deeply weird (Bran doing something, as note the Brotherhood’s cave is full of weirwood roots), possibly through something I haven’t thought of yet. The incident will continue to change Jaime, forcing him to confront events in his past he would prefer to forget, as well as making him deal with Brienne’s betrayal (because she had to, to save her innocent friends). But yes, I believe it’s not part of his personal arc to end Stoneheart, so that’s why I figure they’ll escape, rather than something more… conclusive.
After that, eventually Jaime will reunite with Cersei, I think most likely after she’s fled back to Casterly Rock. Though note I’m saying eventually. I don’t know what Jaime’s path will be between Stoneheart and Cersei because I have not been given enough information that would tell me that yet. (I’ve considered that he and Brienne might be our eyes on the Isle of Faces because someone must deal with that Chekhov’s gun, and they’re the only POVs in the right place, but nothing particular in their stories so far says it must be them specifically. And there’s also the theorized Red Wedding 2.0, though that may be before Jaime and Brienne can get away from Stoneheart.) It’s not my book to write, it’s GRRM’s, and whatever he writes about Jaime before he reunites with Cersei may take all of TWOW if not some ways into ADOS. Or perhaps it won’t. I don’t, can’t know.
Though whatever Jaime’s path may be, his fate and story arc is not tied at the hip with Brienne. She’s got her own story, her own fate, and while it’s certainly associated with Jaime’s story, it is not dependent on it. And vice versa. If Jaime’s story continues after the valonqar – no guarantee there – then he’ll do whatever the continuation of his story may be from the events that have gone before, which could be tied into Brienne’s and/or the War for the Dawn… but if that valonqar climax is within ADOS (y'know, the end), that may indeed be the end for him as well. Nevertheless, it’s still all very wait-and-see, don’t let anyone tell you different.