After having reread through the first book I have come to the conclusion that Lyanna Stark and Rhaegar Targyren must have had an elopement of some sort and/or a child.
Here is the largest piece of evidence, short (as possible) and sweet (and rather difficult to ignore afterwords).
In a Game Of Thrones, Chapter 39, Eddard X,
we begin with the scene at the Tower Of Joy.
Eddard is dreaming of it from the past. He confronts three men, "in white cloaks, and Lyanna in her bed ablood." He is accompanied by six northern men he knew well but sees as shadows in the dream. The three men in white cloaks are Sir Arthur Dayne, Oswell Whent, and Lord Commander Gerold Hightower. They have a brief discussion, in which Gerold Hightower explains that "they made vow's " draw swords and then Eddard and his shadows descend on the three. Ned hears his sister screaming his name, as he is awakened he keeps repeating, "I promise, Lya, I promise."
Now to put it in retrospect.