Lila is in love with somebody who isn't Kiryu.
She genuinely has feelings for him.
Kasumi never thought of the possibility before, why would she?
'Kasumi, I keep falling more and more in live with Kiryu.'
Liar.
'I um want to marry Kiryu.'
Liar.
'I want to be with Kiryu forever, do you think he feels the same?'
Liar.
'I can only sing for Kiryu.'
Lies, it's all lies. All those memories she had with her friend, all those conversations, all of it felt like lies. Kasumi felt betrayed when she heard the news of Lila and Karashima dating. She only felt that betrayal when she saw the two on a program together. At first, when she heard the news while it upset her, Kasumi thought Lila was doing it because of her job. But when she saw that program, Kasumi knew something was amiss.
That's why she contacted Yori and asked her. Yori too seemed upset initially, but Kasumi noticed the more she spoke to her friend for updates, the less mad she appeared.