I know Lilisa is bluffing here, but she’s also right about Maurice Ravel’s Pavane Pour Une Infante Défunte (M. 19, 1910); it is a beautiful piece of classical music (1):

This one shot says everything about how Lilisa wants to be perceived: the perfect young lady, with impeccable manners and impeccable taste and a hair style to match, twin tails so absurd they defy gravity. I don’t understand the people I saw complaining about these in the Anime News Network forums. Of course they’re not realistic nor used for comedic effect; the whole point of them is to give you that over the top impression of an anime ojo-sama. Because that is what Lilisa wants to be.

As her internal monologue immediately afterwards betrays, all of this is pretense. Everybody in the school may be charmed by her persona, but all of it is fake. She’s just a commoner whose mother married into the prestigious Suzunomiya family and it is for her sake that she gave up her love for rock music to devote herself to becoming the ideal Japanese lady, a true Yamato nadeshiko. Because that’s what her mother wants and her new family and school expect of her. Yet as the flashbacks to her pleb past with her father, as well as the not at all subtle intercuts of a caged bird singing show, the pretence is slowly destroying her. In truth, she’d rather eat a beef bowl than the refined French cuisine the school cafeteria serves and rather play guitar than listen to Ravel.

And then she literally runs into the other paragon of ladylike virtue attending her school, her senpai Otoha. Lilisa is immediately smitten with how Otoha seemingly effortlessly embodies the ojo-samaness that takes Lilisa herself so much effort to achieve. As her classmates squeal with delight in the background and roses bloom all around them, she cannot help but look stunned at this apparation. The perfect example of what she’s needs to become if she wants to win the title of Noble Maiden her school grants each year to its most perfect student. But Otoha has a secret, which Lilisa finds out when she finds a guitar pick on the floor near to where they ran into each other.

Because Otoha is a rock drummer who spends her after school time playing in the old school building, absolutely wrecking the drum kit. When Lilisa discovers this and attempts to hand her the guitar pick she found, Otoha goads her into doing a rock duet together. Thinking to put the rich, spoiled girl in her place Lilisa agrees but discovers Otoha is not a pushover, aggressively challenging her into playing louder and harder. Suffice to say that Otoha is far from a perfect young lady once in rock greasy thralls…
The musical performances here are actually done by members of Japanese metal group Band-Maid, who are great and you should listen to. The series is also not afraid to use existing rock music. At one point during Lilisa’s commute there’s a busker murdering the Blue Hearts’ Linda Linda for eample. The performances are CG, which on the whole look decent but do look a bit plastic compared to the rest of the animation, which is decent if not outstanding. The voice acting is great, with Lilisa’s internal monologue offering a neat, raw contrast to her cultivated young lady speech. Otoha too goes from gentle and polite to full aggression and doe4s so perfectly. This is the first series this season that was actually enjoyable not just for the story, but for its presentation.
If you want to judge for yourself, the IMSLP has performances available of both the piano and orchestral version. Do look around the site if your interest for classical and other public domain music is piqued.