Spoilers follow for this week's episode of Game of Thrones. Proceed at your own peril.
Sansa Stark might be bewildered as to why Lord Petyr Baelish would try to kiss her, even if her late aunt Lysa might have seen that one coming. (Too bad she didn't see the Moon Door coming — oops!) As much as Littlefinger has lied, he has also been quite open and transparent about his true motivations and goals — and all along the way, he has never stopped telling us how much he loved Catelyn Stark. Even though he could never have her, Littlefinger has in part lied, schemed, and murdered his way to power so that he could be worthy of her. And now that she's dead, her semi-look-alike daughter is the next best thing.
All the clues have been there since we first encountered Lord Baelish in season one. Catelyn told Ned, "He's like a little brother to me," because little Petyr had been fostered with Catelyn and Lysa, and was raised with them as one of Lord Hoster Tully's own. Although not quite, because Petyr developed quite the crush on Catelyn. During one of his sex-play lessons with the whores in his brothel, Littlefinger remembered, "I was her little confidante, her plaything. She could tell me anything, anything at all. She told me about horses she liked, castles she wanted to live in, the man she wanted to marry — a northerner, with a jaw like an anvil." Not Ned Stark, mind you, but Ned's brother Brandon, Catelyn's first fiancé.
Believing he had a chance, Petyr challenged Brandon to a duel. "Why not? I'd heard all the stories. The little hero always beats the big villain in all the stories." But like Sansa, Petyr's fairy-tale ideas about chivalry were soon shattered. "In the end, she wouldn't even let him kill me," Littlefinger said. "'He's just a boy,' she said. 'Please don't hurt him.' So he gave me a nice scar to remember him by, and off they went." (When reminded of this duel by Ned Stark, Littlefinger calls it a "token of his esteem, from navel to collarbone.")
Even if Littlefinger lost that fight, he never gave up fighting for Catelyn, "a woman worth fighting for," as he reminded Ned, her eventual husband. "You know what I learned losing that duel? I learned that I'll never win, not that way," Littlefinger told his whores in a classic sexposition moment. "I'm not going to fight them. I'm going to fuck them. That's what I know. That's what I am. And only by admitting what we are can we get what we want."
And when it comes to love, Littlefinger has always admitted what he wanted. He told Catelyn, often straight out. He implied it to Ned, who later informed his wife, "He still loves you." And so many people in King's Landing seem to be aware of it — that one time, Varys remarked, "Everyone's aware of your enduring fondness for Ned Stark's wife." (Only Cersei seemed to think this wasn't common knowledge, and tried to use her awareness of it as leverage.)
When Baelish was sent to "woo" Lady Arryn, so that the Vale could be brought back into the fold with the Lannisters and King's Landing, however, it was not widely known that he had already wooed her long ago — that she had helped kill her husband and lied to her sister all at his behest, as we learned several episodes ago. Talk about a twisted love triangle! But Lysa Arryn was only a means to an end for Littlefinger, someone he could manipulate, just as he had manipulated her late husband, the Hand of the King, and other powerful men to give him positions that would allow him to advance further, first, as a customs agent; then, as Master of Coin and a member of the Small Council; then, as Lord of Harrenhal; and now, with Lysa dead, Lord Protector of the Vale. And yes, being aligned with Sansa could be another strategic move to gain the North, but for Littlefinger, this is what love looks like.