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I think she did love Rhaegar. Lyanna is not Sansa so she is unlikely to have fallen for Robert because he was this handsome rich lord the way Sansa did for Joffrey. She saw that beneath the handsome exterior Robert would not be a loving faithful husband. He would make a good friend but a terrible husband and father.
Rhaegar was the son of the Mad King Aerys, and older brother to Daenerys and Viserys Targaryen. Lyanna was the only daughter of Rickard Stark, and sister to Ned, Benjen, and Brandon. Since Jon Snow is the son of Rhaegar and Lyanna, that means Daenerys is his aunt. Since Ned Stark is Jon's uncle, that makes Sansa, Arya, and Bran his cousins (not half-siblings, as they all believed).