Lae'zel will love you for allowing her to go first (+10 opinion) but this is a mistake.
If Lae'zel enters the Zaith'isk. Getting her out with permanent harm to her is difficult.
Your first opportunity to get her out requires rolling a nat 20 on either a Persuasion Check or a Wisdom Check - if you succeed she will exit the machine unharmed, the machine explodes, and Lae'zel will believe an unknown actor sabotaged it.
Never click the "Wait" option, it's no different to the "Endure" options but at least the "Endure" options give you approval from Lae'zel (+1 opinion each time).
If you tell her to "Endure", you can make a DC 21 WIS check, or a DC 30 Deception check, "Endure" again, or "Wait" again.
The WIS check reveals the Zaith'isk doesn't remove Tadpoles, it kills the infected. This unlocks a DC 21 Persuasion check to get her out, she will have a minor permanent debuff even if you succeed.
The Deception check requires a nat 20, if you succeed she gets out with the same minor permanent debuff.
If you tell her to "Endure" again, you get the following options:
A DC 30 Deception check
A DC 30 WIS check
A DC 21 CON check
A DC 30 Arcana check
Endure
Wait
All options will result in the destruction of the Zaith'isk and Lae'zel receiving a significant permanent debuff.
The Con check reveals the Zaith'isk kills the infected rather than removing the tadpole and unlocks the same DC 21 Persuasion Check as before.
The "best" option is the DC 30 Arcana check, as while it cripples Lae'zel like the other options, at least your character gets a good permanent buff out of it, just remember it requires a nat 20.

The truth is that letting Lae'zel go first is sub-optimal. Your character should go first.
If you make the 3 Saves, you get the same permanent buff the DC 30 Arcana check gives you, except you don't have to cripple Lae'zel to get it. The DCs are 12 INT, 15 WIS, and 18 CON, failing any of these gives similar permanent debuffs as what Lae'zel would have suffered. I don't think you get the buff if you fail any of the Saving Throws.