Some early morning musings:
In this ASOIF Wiki Page
, they theorize that Rhaegar thought he was the Prince that was Promised. In addition, he seems to have referred to the phrase "song of ice and fire".
I wonder if it was something in this prophecy and his trying to fulfill it that drove him towards Lyanna Stark? Right now it seems as if their attraction was all about romantic love. (of course at the beginning of the series, it was implied it was all about him kidnapping her against her will, so appearances change).
I guess it's possible that Rhaegar was trying to fulfill the prophecy by merging ice (ie: Lyanna Stark) with fire (Rhaegar Targaryen) to create: Jon Snow? as the prevailing frame of thought is R+L=J.
Of course, the fact that in the House of Undying vision, Rhaegar seems to have been referring to his son Aegon by his wife puts a damper on this theory. But of course, it's pretty well established that prophecies can be twisted or not 100% accurate in this universe.
This post was edited on 4/7 at 7:15 am