Of course WE know that everything Littlefinger does is to his own ends, but Littlefinger went to the Vale on the orders of the Lannisters in the first place. He whisked Sansa Stark away from the Lannisters, and while Sansa maintained her fake identity the Lannisters would have thought Littlefinger still loyal to them. But it's been many episodes since Littlefinger declared Sansa openly in the North, then the Boltons married her to Ramsay Bolton. And everything Roose Bolton and then Ramsay Bolton have done since then indicates that they intend to rule the North without allegiance to the Iron Throne.
But so far I haven't seen any mention of it in King's Landing. They haven't made any moves based on it, or even discussed the fact that that they've lost the Vale and most of the North again along with the allegiance of House Bolton. Is it supposed to be that word still hasn't gotten back to King's Landing about it? Or are the Lannisters conceding the North? Or did I miss something?