Not sure if you already found her or still care, but from my experience:
- I have a magic skill of at least 400 before getting my first paycheck. This is so that the magic shop is unlocked and I can buy the memory ward. This ward isn’t necessary to meet Lexy, but is necessary to keep her around
- I have a coding skill of 750 or more, on the day you don’t need to go to work. So the same day you get the paycheck
- When Fexa asked to speak with you in private, I chose to meet her in the VIP booth. Once there, I rescued her due to my coding skill and Lexy soon appeared to congratulate the attempt