Dazai was in the mafia, yes but Mori still made him go to school and get an education. Of course, he didn't get the full student in Japan experience because it didn't really matter—he didn't go to extra lessons, he wasn't under any significant pressure for grades but he still always got almost a full score. He was second in the class.
Lysandra was the first in class— she got the maximum score in every class. But she wasn't a goody two shoes— Dazai hadn't seen her attend a math lesson even once but the teacher always marked her as present and gave her good grades without her even doing the tests. She clearly had significant blackmail on the teacher. She also sat on the first desk, in the left side of the room, right in the literature teacher's blind spot, who had reduced peripheral vision on that side and didn't even realize it. Lysandra had figured it out faster than Dazai and exploited it— she did anything but pay attention in that class yet the teacher spoke very highly of her and praidsed het analysis skills.
But Dazai noticed how the small, minute details of her life changed with each teacher— she was telling them whatever they would like to hear, which she deduced from the small things about them. She had a manic charm to her.
Lysandra was also relatively popular and charming, but she only had two close friends from that class. But she knew a lot of younger and older people from the school. She was friends with everyone so nobody would rat her out on anything— she was the closest to people most likely to do it. Everything about her was so calculated and purposeful.
Dazai had his impression of her: very manupilative, very observant with some psychopathic traits. Dazai felt like he was looking into a mirror. She was also friends with him and even if they weren't close, Dazai knew she was keeping him as close, as she wanted him to be.
The persona he took in class was the silly, slightly stupid guy who somehow got really good grades. He lied about his family life and lied about his ambitions but he felt like Lysandra could sniff his true nature out, just like he could sniff her out.