I don't think it's a bad call to have your whole party confront the Gith. You're trusting Lae'zel...
Agreed completely, if you play Githyanki yourself ...
Have some reservations if you dont ... but still agree it is possible (in certain scenarios) to thrust her.

The dragon and rider leave for no good or logical reason. I'd like a better reason, please.
Agreed 100%, twice around and even more!
And finally, Lae'zel doesn't learn. Afterwards, she just blindly believes if we go to her creche, her people will cure her. Even after all that, she still nags you to go to the creche?
I really dont want to bring real life politics into this ...
So please try as hard as you can to take this as pure theoretical example, not attacking anything personal ... i just say this bcs i believe it should be close enough to you, to understand my point ... okey?

I know you are very religious person GM ...
Now imagine situation, that i would show you
single high-rank priest, that is pedophyle, and is sexualy abusing young boys, using church as a cover up ...
What would you presume?
- That the whole Church is rotten, completely corupted, and you should refuse them completely?
- Or that this one person is rotten, and abused this rightfull organisation to his own lowly desires?
That is why Lae'zel "didnt learn".

She simply presumes (and quite logicaly from her point of view) that Kithrak is corupted asshole, who makes really bad name to her people.