On the issue of Triss "betraying" her sisters of the Lodge, I have to say that the Lodge threw her under the metaphorical bus, and Triss was practically no longer a member by the events of Witcher 2.
The 1st break between Triss and the Lodge is at Montecalvo when the senior Lodge members don't let her talk to Yen alone. Francesca is watching Triss like a hawk the whole time.
The 2nd break comes when Philippa orders Triss not to help Yennefer when Yen calls her by megascope. Triss shows weakness by not standing up to Philippa, but she sees the consequences of the Lodge's "mission".
The 3rd break is during the Battle of Brenna- Triss states that she was explicitly forbidden from joining the fight, even though it is a cause she believe is (the freedom of the Northern kingdoms).
During the peace conference in Cintra we see evidence of a 4th break:
"... Ciri, the heiress to the throne, the young lion with the Lioness’s blood... Ciri, my little sister. Who is now apparently far away to the south. Fortunately, no longer alone, she is with Geralt and Yennefer. She’s safe. Unless they have lied to me again."
So already by the end of the books we see that Triss is feeling betrayed and lied to by Sheala, Philippa, and the others. Then we get to the events of the games, where they exclude her from meetings and don't tell her about their assassination plans. If they had told Triss about Letho and the plans for Demavend, Triss could have told them something was going wrong when the first witcher assassin tried to kill Foltest (in the Witcher 1 epilogue). There might have been time to stop Letho, save Foltest, and prevent the collapse of Temeria. Instead the Lodge left Triss in the dark, so all the work she did in Vizima disintegrated when Foltest died (She tells Philippa "5 years of my work gone.")
Originally Triss was fully committed to the Lodge because she believe in the mission, but by the end of Witcher 2 she sees that the Lodge has lost its way and become a destructive force. Triss and those close to her became collateral damage because the Lodge lied to her and excluded her from their plans. Why should she remain loyal to them? Why not throw Sheala to the wolves to try to give other mages a chance with the new Conclave?