Board Thread:TV Show Discussion/@comment-1399600-20170609041431/@comment-28669501-20170624131813

The point of Dragonstone is to protect the heir until their ascension to the Throne thus the title "Prince/Princess".

When Stannis took the castle he was Lord of Dragonstone because he wasnt the heir.

With no heirs to the throne and Daenerys be the only Targaryen her title is Lady as she is not and heir.