Many people who subscribe to the Rhaegar + Lyanna = Jon Snow theory also seem to assume that Jon Snow would be the true heir to the Iron Throne.
However, is that how succession really works?
Even If R+L=J were true I dont think Jon would have a strong claim to the Iron Throne.
Rhaegar as crown prince was the KING's heir, and he also held the title Lord of Dragonstone.
However, Rhaegar died BEFORE his Father. Therefore he never became king and never inherited his father's claim to the Kingdom of Westeros.
The only title Rhaegar's children could then inherit would be the Lordship of Dragonstone.
The crown would then have passed to the KING's next born son Vicerys. Which is exactly what the book reads.
Many R+L=J believers seem to think the crown would pass to the Prince's son. And many state the Kings guard's presense outside the tower of joy as reason. However, that doesnt make sense. Why would Aegon or Jon inherit the King's crown if his father was never king. Vicery's Father was the king.
This ultimatley makes Daeny's claim much stronger than Aegon or Jon's.
however, they both (if they are real Targaryens) do have a claim to their father's title, Lordship of Dragonstone.