In The Swallow's Tower Yen said that she'll never forgive Triss for siding with the Lodge,so she obviously cared about it:Yennefer didnt care about Triss being in the Lodge, she only used it, that Geralt will never forgive her for that. That fight was only because of Geralt: "Dont think you are going to meet a loved one Triss..."
“The information,” Yennefer said dully, “for his life. Save him, Philippa.”“No, Yennefer.”“Because it's not in the interest of the Lodge.” A purple fire kindled in the sorceress’ eyes. “Did you hear that Triss? There, you have your Lodge. You see their true colors, their true interests. And what do you think of them? You were a mentor to the girl, almost – as you put it – a big sister. And Geralt…”“Do not attack Triss’ relationships, Yennefer.” Philippa retaliated with her own fire in her eyes. “We will find and rescue the girl without your help. And if you succeed, that's fine, a thousand thanks, because you will have saved us the trouble. You tear the girl out of the hands of Vilgefortz and we will be happy. And Geralt? Who cares about Geralt?”“Did you hear that, Triss?”“Forgive me,” said Triss Merigold dully. “Forgive me, Yennefer.”“Oh, no, Triss. Never.”