That prompted Robert Baratheon to wage a war against Aerys Targaryen and eventually winning for him the Iron Throne.
Rhaegar kept Lyanna at the Tower of Joy in Dorne before leading his army in the Battle of Trident where he was eventually killed by Robert Baratheon, details the International Business Times.
Ned Stark went south to get the last holdouts to pledge fealty to Baratheon. He arrived at the Tower of Joy to find three knights of the Kingsguard and a battle ensued. After the battle, only Ned Stark and his best friend Howland Reed survived. Ned found his sister Lyanna dying in a bed of blood apparently after giving birth to a boy. She also has a dying wish. The secret was accordingly Jon Snow and she made her brother promised that no one will know her and Rhaegar’s secret.
Apparently, Lyanna was not kidnapped but she and Rhaegar were actually in love. They actually eloped and were trying to flee from their respective responsibilities in their respective kingdoms and decided to settle in Dorne. Their love has brought forth a son, which Ned eventually claimed to be his bastard son.
With that being said, Jon Snow is actually the niece of Daenerys Targaryen as the Queen of the Dragons is the younger sister of Rhaegar.
Based on the photos and trailers of Season 6, the Tower of Joy will indeed be featured but it is still unclear whether the TV series will delve deeper into the theory or reserve it in the next season or Season 8.