That theory is well known for game of thrones scholars. But I love hearing it every time so thank you. The whole events during and leading up to Roberts rebellion is shrouded in mystery. It was the turning point in the world.Lyanna Stark is actually the knight of the Smiling Tree. The knight of the smiling tree is from the tournament in which Rhaegar places the crown of roses on Lyanna's head instead of his wife Elia Martell.
The knight of the smiling tree fights three bannermen and unseats them all three. To earn their belongings they lose after being challenged the bannermen must simply "teach their squires some respect". The squires are beaten. Why is that important? Because Howland Reed is being attacked by three squires of these bannermen and Lyanna stops them initially. I feel Lyanna dressed as the smiling knight to gain justice back for their friend Howland Reed.
Nobody knows who the smiling knight is. And just like that the knight leaves the tournament. The mad King thinking that the knight must be an enemy plotting his end send Rhaegar to hunt the knight down. It is also noteworthy that the mad King makes his first appearance outside the red keep on four years at this tournament. Rhaegar does so and returns with only the shield of the knight. Why you ask? My theory is he tracks the knight down and figures out that it's Lyanna and he is both impressed with her skill and beauty and Firey personality.
Rhaegar lets her go and maybe they have some sort of love triangle deal going on at this point? Either way Rhaegar lets her go and returns to tell his father the mad King he only found the kinght's shield. After Rhaegar wins the tournament and places a crown of winter roses on Lyanna Stark, passing up his wife Elia Martell it is obvious he has his sights on Lyanna. Then things get uncomfortable.
Rhaegar and Lyanna run off together not long after the tournament. Lyanna doesn't realize anyone will think she's kidnapped and she doesn't want to marry Robert because she thinks Robert is a whoremonger who will never be faithful to her. Eventually her dad and brother get killed and she gets pregnant and is afraid to show herself.
Robert kills Rhaegar in single combat and then when Ned and company come to the tower of joy she has just birthed Jon Snow and is expiring from the labor. She makes Ned promise he won't tell Robert and that he will take Jon and care for him. Ned being Ned does as he promised his dying sister and low and behold we have us a good story to watch or read.