more info:
So firstly, Lily is on the opposite team, and her team being always against Mao's team
While she's always on 2nd or 3rd place, she ain't too upset.

But the reason the beef between her and Mio started is all over an misunderstanding
Mio often loves to gossip to Mao and when she gave a description of half dyed hair, she thought Mio was talking about her when it's about an completely different person.