Family Trees!
All right, the Family Tree page is updated for Martells, Starks, Targaryens so their genealogy goes back a bit further and thus explains the line of succession, which is, (as currently defined by the Citadel) btw:
Jaehaerys Rhaeys Aenyris William Stark Brandon Stark Elixabet Stark Genna Stark Lyon Stark Kyle Stark Lilyanna Lannsiter Tyronne Lannister Jaremy Lannister Toria Lannister Lyanora Stark Rodryk Tyrell Rosaline Tyrell Euen Stark Aeria Martell -- excepted due to already being queen Myrwin Martell Henry Martell Karlyx Martell
Please note that since Daenerys reclaimed the throne, actual Targaryen tradition was reinstated (overruling the effects of the first Dance of Dragons) and the throne can pass to a firstborn girl ahead of a secondborn boy... that would actually boot Lily and her family up ahead of William, or later could lead to Elix inheriting ahead of Brandon.
This is the line of succession set down by the Citadel in order to establish the Regency. ...