Oh, I don't think Littlefinger just merely knows that Rhaegar didn't kidnap and rape Lyanna and that they were really lovers--I think he had a hand in helping Rhaegar and Lyanna run away together. After all, Littlefinger's whole deal is to secretly cause chaos in the realm in order to advance himself, and certainly arranging it for the son and heir to the Iron Throne and the daughter from the greatest of the Northern Houses to run off and elope together which resulted in an all-out civil war between the Seven Kingdoms would right up his alley. Not to mention look what Littlefinger was able to get out of Robert's Rebellion--he became Master of Coin, thanks to his seducing Lysa, who just so happened to be married to Jon Arryn, the Hand of the King appointed by Robert.
And the other reason Littlefinger could've arranged for Rhaegar and Lyanna to run away together? Remember, he tried to fight Ned's older brother for Catelyn's hand in marriage and lost. And we know that, deep down, this really hurt Littlefinger's pride since he's been in love with Catelyn from the get-go, and probably was thinking "I'll show them! Nobody humiliates me like that and gets away with it!" And, having observed first-hand Rhaegar's affection for Lyanna at the Tourney of Harrenhal, thought to himself, "Aha! That's how I'll get back at the Starks. And seize a little opportunity for myself in the bargain."
Now whether he also knows Jon Snow could be the son of Rhaegar and Lyanna is another matter, but it wouldn't surprise me if Littlefinger, being as clever as he is, at least suspects the truth about Jon's true parentage.