Strange- I've done this part several times since Hotfix 10 dropped and letting Lae'zel go into the zae'thisk, or losing the rolls to tell her no, always worked. Are you on PC and using any mods?
I'm playing on PC. I don't mod games. I walk up to the Zaethisk and Laezel says "you deny me my right to go first" but the conversation where she actually demands to go first and I let her is missing. All I can do is control her and walk her up to the machine, where she gets in and the whole sequence plays out without any saving throws or persuade checks. It just blows up and she gets all 3 penalties. She's always in my party and has a good approval rating (the marker is past the L in Approval).