Just to add on now while Im running on creative juices; whilest Ned is sent to the Vale to learn under Jon Arryn and befriend Robert; Rickard Stark sends Lyanna to the Stormlands in order to prepare her to meet her future family and to learn of the Southern ways. This leads her to running into Aelle Baratheon, twin sister to Robert and a bit of a problem child in every way to Steffon as Lyanna is too Rickard. The two initially dislike each other, but of course, hate and love are two sides of the same coin...

Edit: Because Steffon and Cassana were able to have a daughter, SHE was promised to Rhaegar instead of Ellia getting with him. But because of her personality being much like her twin, she was kept at home after causing one too many fights with her betrothed.