LF sacrifice himeself? No way IMO he is way to selfish.
I'd like to think that he'd do it out of his love for Catlyn.
I don't think Littlefinger has any reedeming qualities. Varys' quote about him "He would let the world burn if he could be king of the ashes" may be entirely accurate. Sure he wouldn't mind if Sansa is alive and well but there's no one in Westeros and Essos he'd die for, for me.
What about this series makes anyone think that the Starks will win the battle? I wouldn't be surprised if Ramsey ended up killing Jon Snow and recapturing Sansa. With the way this show has gone, that seems much more likely than the Starks winning.
Even from a non predictable narrative standpoint, it doesn't make sense to kill Jon Snow, resurrect him and then let him die again. Jon also is clearly shaped up to be one of the key players of the endgame, and he just can't die before he, or at least the audience, discovers who his real parents are.
Also, the White Walkers are clearly and surely gonna invade Westeros one way or the other and what's the point of having Ramsay holding the north when he's gonna be icy-trampled to death anyway?
Surely it won't be an entirely happy ending, and even if it is, it will be a short lived happiness when the White Walkers will invade, but the battle for Winterfell is the last time a character like Ramsay is needed.
Then again, we're all none the wiser and we shall see, Ramsay could lose the castle but escape, kill a lot of good guys before falling etc, but I would be very surprised if there's still the Bolton banner on top of Winterfell when the season ends.