If Miss Bustier reached out to Lila's parents about her continued absence from school:

It occurred to Miss Bustier that Lila's position as a student of the school was likely on very shaky ground at this point because of how much travel her parents were taking her on. She never realized that ambassadors changed locations so frequently... In any case, taking their daughter on all these trips was all well and good for teaching Lila about other cultures but it was causing havoc for Lila's grades. She was constantly turning in assignments late or incomplete and it could not be good for her learning.

Thus, Miss Bustier decided to reach out to Mrs. And Mr. Rossi to try and convince them to let their daughter come back to Paris and start attending school on a more regular schedule. A quick chat with the principal and the two of them agreed to call the parents together during the next lunch break (Lila hadn't said where her family was going next but unless it was Hawaii then her parents would likely be up and about working, getting ready for work, or finishing work).

The first attempt to call Mr. Rossi failed and the two of them left a cheerful voicemail informing him that they would just like to speak to him about his daughter's homework and class attendance. The next call, to Lila's mother, got through.

The conversation was not what either party expected.

For some reason, Lila's mother had been under the impression that the school was shut down due to all of the Akuma attacks and that was why her daughter was being kept at home. The more the conversation went on, the worse it seemed to get.

Lila had lied to her parents about the school being shut down and the school about traveling the world just so that she could stay home from school (which meant she had no reason to be turning in such shoddy homework Miss Bustier grumbled internally). In fact, Lila's mother informed them that Lila had only ever visited Italy and France because her parents, as it turned out, were not very big into travel.

The agreement the three reached in the end was that Mrs. Rossi would get her daughter to start attending school again and the teachers would keep a close eye on her daughter for another other lies or attempts to get out of doing any work. The three also agreed to have either Mr. or Mrs. Rossi physically come to the school to fill out any paperwork pertaining to her daughter or have one of them call the principal about anything involving their daughter. Lila had proven that signed documentation from her parents could no longer be trusted since the last papers they had received from the Rossi family declared that they were taking their daughter on an extended trip outside of the country.

AN: Yeah, I find it hard to believe that Lila was gone for weeks and the school was just fine with her missing for so long and didn't even try to call her parents to talk about the situation. Her parents believing the school was closed and not even double checking on that? And them not getting any emails/calls from the school about any events that happened during that time like board meetings or parent/teacher conferences or anything? Yeah, very unlikely.