Sorry, but I just can't see Yennefer betraying the Lodge, even Philippa.
We have seen in the game that she even asked Emhyr to grant the Lodge amnesty for helping, she does care what happens with them.
In the books there is of course some kind of rivalry between all of them, but they never hated each other to a degree that they are willing to kill each other or sacrifice their lives for their own good.
Even though the Lodge tried to use Ciri in the books, Yen still went with Ciri to the Lodge to talk, because that's reasonable.
Those are reasonable women (and men) and for all of them their own kind, sorcerers, is more important than this personal grudge. That's one of reasons why the lodge was created, to protect magic in this world and I doubt anyone from the Lodge would disagree.
No, Yen might be proud and reckless when it comes to Ciri, but she would never betray her own kind for that matter. It's like saying Geralt would kill Lambert to save Ciri, that's just bullshit, even though he is a prick.