GrimGrimoire/WMG

Lillet actually planned everything, in order to become a "magnificent magician" as well as gain a happy life.
The game leaves out how Lillet became tied to the Philosopher's Stone in the first place on the first day, just finding it would be an action that would have required her to smash through the walls of her room and then get past Master-class wards without having any previous knowledge to do so.

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.

Lillet was related to the Archmage.
As pointed out, considering how the Philosopher's Stone was hidden, the fact that she likely held little to no magic ability at the time (If she was lucky, she might have been able to use elves), and the fact that even after being opened the area around the Philosopher's Stone was heavily trapped enough that even a master magician would have trouble getting through it, she would have had to know how to disable the traps and possibly open a secret door, implying a connection to the area beforehand. In addition, Lillet's first meeting with the Archmage includes some fairly interesting dialogue: He seems to imply that the one Lillet should be scared of is Gammel.

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.

Amoretta either allowed herself to become a homunculus or was found injured to the point that no other form of recovery was available.
While Chartreuse may be slightly amoral For Science! at times; he wasn't evil. Even with demons as teachers, just flat out taking an angel's soul would be out of character for the school.

Advocat gets far more mage souls by not asking for them then any other devil does trying.
Clearly one of the rules of conduct in his bet with Gammel is to not initiate any Deal With the Devil contract for souls with the students at the Silver Tower. However, the fine print is that it's fine if said student initiates the deal; as seen in his dealings with Bartido and Lillet. Ironically this method works better than scheming; as that would scare people off. Just the Forbidden Fruit knowledge that he can give them anything they want is enough for some students to meet with him in secret; and he's "bound by Devil/Client Confidentiality" not to reveal if anyone has. Likewise, he has to forestall any This Is Your Brain On Evil sideeffects or else Gammel would find out...and this also means it's far more likely for people to make deals with him. No bad publicity.

Advocat still had the contract regarding Lillet's soul
Lillet figured that Time Travel would negate the Contract...but Time Travel doesn't negate Grimoires...so why should it negate Contracts?
 * 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.