So much of the plot of GoT revolves around two people that are barely on the show. There's a huge divide between what people who have read the books and those who haven't on the topic and a lot is left to guesswork. So using everything but season 7 spoilers (be good), let's try to find some answer.
My question is: what was Rhaegar's plan? It could be assumed that the Tourney of Harranhall was all a setup to potentially overthrow The Mad King. Then Rhaegar gives Lyanna the wreath and a year later kidnaps her. Or they elope. Something.
At the end of Robert's Rebellion, young Ned and his mates show up at the Tower of Joy and find Lyanna and newborn Jon Snow protected by Rhaegar (who is dead now)'s best soldiers and his bestfriend. So, back up a minute. What was Rhaegar planning to do with Lyanna if he won and got control of the crown? The loyalty of the Martells was critical to his success, did he think that he would just show up with his new family and they'd be ok with the cuckolding of their sister.