Lady Stoneheart may never appear on Game of Thrones, but it's possible that her quest is being fulfilled on the HBO series through another character. Arya and Lady Stoneheart's Game of Thrones' storylines are eerily similar. There are spoilers for A Feast For Crows ahead.
The Season 7 premiere made no bones about what Arya's mission is upon her return to Westeros. She's going to kill Cersei, and she's going to take down every Frey and Lannister man she can in the process. That happens to be the same mission that Catelyn Stark adopts when she is brought back to life by Beric Dondarrion in the books.
If Arya's storyline is borrowing from Lady Stoneheart's this season, that could mean danger coming for some of your faves. In the books, Stoneheart attacks Brienne and Podrick. She asks Brienne to kill Jaime Lannister, and hangs both Brienne and Podrick when Brienne refuses. It's unknown whether or not they survive — the scene ends with Brienne shouting out the word "sword" in an attempt to stop the hanging. I hope that Arya wouldn't be so single-minded that she would threaten these two sweet characters just because of their association with House Lannister, especially after all that they've done for both Jon Snow and Sansa Stark.
While I think this would be a cool way to finally bring Lady Stoneheart to the HBO series in an organic way, I'm also not thrilled about what it would mean for Arya's humanity. I want her to be with her family again. I want her to think twice before slaughtering Ed Sheeran and his jolly band of Lannister boys. I'd rather see more face-stealing and elaborately staged mass murders than a hooded killer who shows no mercy to a fault.
At least Lady Stoneheart had being a lowkey zombie with extreme vocal fry on her side. That justified her ruthless ways. Arya is still a living, breathing human being with a full heart and a decent set of critical thinking skills. I'd just like for her to stay that way, physically and metaphorically.