The only game ending answer is the trollish one
where you tell Vlaakith, if she is so powerful, she can do it herself
Otherwise you can deny it
, Vlaakith vanishes, but leaves the portal to the astral plane open and you can talk to your Guardian, who has interesting news about Vlaakith. When you share the news with Lae'zel, she agrees to let the Guardian live. The whole Gith base will be hostile after that though
Or you can just skip all that, keep playing the game and change Lae'zel's mind later! Did that yesterday, it was great. My only regret is missing part 2 of the book on Orpheus.
