I think that likely only Robert and maybe Ned (thought his older brother and Father likely knew) that Rhaegar hadn't actually kidnapped and rapped Lyanna. If 3 people knew, and two of them are dead; the last person I.E Robert....can say whatever he likes and everyone will believe him because Raeger and Lyanna were to busy missing from action to be ably to defend themselves. We also won't know what Rhaegar told his men, because they all died or most of them did. My bet is if any of the survivors knew the truth, they probably knew to keep it to themselves.
IMHO, I think Robert absolutely knew the truth, but he chose the narrative that allowed him to wage his war against the Targaeryens. If he choose the truth, his options were to be a jilted man spurned by Lyanna Stark, and have all of Westeros know that she ran out on him for another man and the Starks broke faith and say or do nothing about it; or go to war with the Starks, his best friends family, over it. Robert doesn't seem the man to idly sit by why the woman he covets runs away with another man.
We also know, from Gilly reading the diary, that the Maester who annulled his marriage and married him to Lyanna did it in secret. So no one knows about it.