So, what if Lyana Stark had black?
She didn't since hers was brown like all of the other Stark's
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You have to remember that Robert like to drink to much and…
It is easy to see where that led.
Rhaegar was not in love with her since he already had a wife.
He was protecting her from Robert which is why Ser Arthur Dayne was down where Lyanna was at while giving birth.
Rhaegar commanded him and the other Kingsguard to protect her.
Which is also why he wished Ned Stark
good fortune in the wars to come
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Since Ser Arthur knew how Lyanna ended up pregnant and that it was not by Rhaegar.
She told Ned everything and Ned knew what would happen if the real truth got out.
Which is also why he decided to stay in the North rather than go to Kings Landing and help Robert.