And she did give her daughter's soul a new body to inhabit.
In fact, Liandrin's soul was in perfect control of a body. It was only until the assessment tests that the need arose for her to swap into a new vessel.
That was when Arianna had become a potential target for Thamoryn's soul branding.
She needed someone beautiful and of respectable background; someone who might be able to make the right people listen.
The right people in this situation were the new intakes: Aiden, Laela, and Ambrose. Although Kayden was still a good bonus.
When she had successfully lured and captured the unsuspecting Arianna, she then directly moved Liandrin's soul from the body she had initially possessed into the body of the Greystone.
Liandrin, now awakened as Arianna, was instructed to keep watch on them while helping with their development.
So the part where she had told Aiden about her goal being to achieve the title of Grand Magus; that part was all a lie.