Board Thread:Questions and Answers/@comment-28572384-20160528002422/@comment-5014364-20160528004729

Historically the Targaryens practiced polygamy when they thought they could get away with it. Aegon the First was married to both of his sisters, simultaneously. As the theory goes, Aegon could easily have secretly married Lyanna.

Big part of the theory is that Rhaegar was convinced by a prophecy that he needed to have three children who would save the world. But his wife Elia Martell nearly died from her two pregnancies, and the maesters stated in no uncertain terms that she would absolutely die if she ever got pregnant again.

Thus, Rhaegar probably sought out someone else to have a third child with. As for Elia....the Dornish have been known to have both a lawful wife and a paramour, simultaneously, and be okay with that. So we're not clear if even Elia might have been okay with it.