Betrayal doesn't require swearing allegiance, it requires trust. I might be wrong but from what you wrote before, it sounds like you allowed the Emperor to suck out Orpheus's brain while being on the rebellion path with Lae'zel in which she along with Voss and the rebels wants to free her people from Vlaakith, and for which they deem Orpheus necessary. They trust that you free him and if don't but side with the Emperor instead, they are understandably upset. Poor Voss tried to free his friend and prince for how many centuries? I forgot but it was a long term project.
I told her "we'll see". I didn't promise her anything. I expected the game to offer more choices beyond “him or him.” I said I was entirely on the Githyanki side and would do everything to help them, but I never ever promised to exchange the life of my most important ally for their Prince. So no, I didn't betray her trust.
Even with Orpheus gone, there were still paths to defeat the Queen that didn’t require killing my allies - and I would've backed them completely. But no - they demanded I do exactly what they said: free Orpheus. That's manipulation. How the hell could I be sure that freeing him would help us defeat the brain, or help overthrow the Queen? And Lae'zel threw another tantrum "I regret not killing you in the camp". Thank you, Lae'zel. Had she killed me at the camp, her pathetic ass would've ended its existence in that brain machine in the Creche. Screw the sunset scene in the Lower City and the 100 approval. Why is she simply incapable of such basic reasoning as a sapient creature?
She'd make a great pitbull-style NPC - aggressive, dumb, and relatively loyal. But as a main companion? Maybe if there were more satisfying GTFO mechanic available throughout the whole game - not just at the beginning - and a wider selection of female companions to choose from, I'd be happy. But with only Karlach not periodically getting on my nerves, I'm not.
