After killing the bigger part of House Frey, Arya Stark travels South to King's Landing, to finally cross Cersei Lannister's name from her list. Simply travelling there is already hard enough as it is, though, so actually getting close enough to kill the Queen might not be as easy as she hopes. Perhaps what Arya needs most right now is the help of a dragon.
After ending her time with the Faceless Men, Arya can finally go home. However, with the coming war against the White Walkers, Winterfell might not be safe for long. The Stark's best option: to ask the Targaryen princess for assistance when she finally wins the throne. Arya isn't very patient though, so she decides to give the dragon's army a hand in taking King's Landing, and maybe cross a few more names off her list while's she's at it. Actually crossing Daenerys Targaryes while on her mission wasn't really her intention, but the Gods sometimes have strange intentions for their people...