You see, the Lillet we know is VERY different from who she used to be....thousands of years ago last week.The answer is such; she knew that the Philosopher's Stone was there, and intentionally bound herself to it. This would give her infinite access to the Silver Tower's magic research, and any grimoire she wanted via a Deal with the Devil. The time reset would automatically reset any Demonic Contract as well, but the magic and knowledge would remain in her soul. (Which she could sell again the next reset. Hundreds of Faustian bargains weaseled out of and Hell doesn't even know.)
All that remained is her mental well-being. That much time would make most people go insane; so she split her personality and shunted off parts that started to decay into the void surrounding the Philosopher's Stone; as well as rewriting her own memory and personality. Eventually she acquired enough power and the ideal personality that she wanted to both defeat the Archmage/Demon combo and have a happy, comfortable life after. And she's not even aware of most of what she had to do for it.
Keeping in mind that when she was admitted to the academy, she was an orphan living in the middle of nowhere, apparently doing little more than taking care of her relatives, it's unlikely that she would have been admitted unless someone at the academy already knew about her.
As such, this troper suspects that Gammel admitted Lillet to the academy entirely to pull off a Xanatos Gambit of his own in an attempt to find out where the Archmage hid the Philosopher's Stone. However, by the time she managed to find it, the Archmage was released and eliminated Gammel, preventing him from swooping in at the last second and use it for his own ends.
- The only problem with this theory being that Lillet is not an orphan, as the Epilogue clearly states that her parents are proud of her. Having parents = not an orphan. Also, Gammel mentions that Lillet was a student at the Magical Society before being selected from there to go to the Magic Academy.
- Easy. She was adopted. Also, the "Magical Society" was something Gammel guessed at being a possible explanation for Lillet knowing the spells she does in the second timeline, and she went Sure, Let's Go with That. (Since Time Travel never occured to him) She "borrowed" this explanation as something he would believe when she got even better at magic in later timelines.
- However it has expired. The deal was for him to take her soul one week after letting her borrow the Lemegeton. He doesn't remember the contract, he doesn't remember giving her the Lemegeton, and she gave it back to him early. He thinks it is some kind of trap. He's somewhat paranoid of her mad demon-dealing skillz and has just decided to ignore it; if she doesn't bring it up, he won't either.
- If Contracts still exist, this also means Lillet's name is suddenly on any other deal she made in the thousands of years of her "Groundhog Day" Loop. It would be a massive Enemy Civil War in hell to actually try to sort it out, especially since nobody remembers her making such contracts in the first place, so it could be viewed as some weird "glitch in the system." John Constantine, eat your heart out.
- You're all forgetting the fact that when Lillet asks Advocat about Bartido's contract, he denies "consorting with him". So, maybe, only the things that Lillet herself owns are what travel back in time with her, since she's the only one affected by the loops.
- That could also just mean that since Advocat doesn't remember the contract, he doesn't know to collect. Or, of course, Lillet's soul could still be affected by the contract when other people aren't because her soul, unlike theirs, is going back in time. (But either way, as noted, Advocat doesn't benefit because the wording of the contract means he has to actively claim her soul and he doesn't realize he can; possibly Lillet set it up that way intentionally just in case.)