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At the tourney at Harrenhal in the year of the false spring, Rhaegar won the jousting contest. But instead of crowning his own wife Elia the queen of love and beauty, he crowned Lyanna.
It seems that Lyanna did not truly love Robert, and Rhaegar was not the evil man who Robert made him out to be.
In this two quotes:
Yet sometimes Dany would picture it the way it had been...Her brother Rhaegar battling the Usurper in the bloody waters of the Trident and dying for the woman he loved...
GoT, pg. 30
Rubies flew like drops of blood from the chest of a dying prince, and he sank to his knees in the water and with his last breath murmured a woman’s name...
CoK, pg. 706
GRRM avoids using the word ‘Elia’ and instead uses ‘the woman’ or ‘the woman he loved’ suggesting that it could be someone besides Elia... Lyanna, perhaps?
When Eddard went to the Tower of Joy to save Lyanna, there were three men of the Kingsguard (Ser Arthur Dayne, Ser Gerold Hightower, and Ser Oswell Whent). This is curious since, as far as the reader knows, there is no royal blood present at the Tower of Joy, just Lyanna. Then why are they there, instead of with Viserys or Daenerys? (Rhaegar and Aerys are dead by this time.)
And all those "Promise me, Ned" around the books... Seems to be something deeper that just being buried in Winterfel...