I remember that, when the novel revealed the 'Layla is a pervert' twist, the comments were suggesting ideas about what the deal with her was. There were four basic ideas:
1. Layla is a perverted man, who reincarnated as her. He is now taking the opportunity to do stuff with girls (It wasn't just Sarah in the novel).
2. Layla is a perverted (and predatory) lesbian. Same logic applies as before. While a humorous concept, this is unlikely (unless the author intends to make her into a villain).
3. Layla's preference is determined at the start of the 'game', with her gravitating toward the type of person who gave her the most attention. In this case, that person is Cecil (the novel puts more emphasis on Cecil's rumored interest in Layla, and Sarah explains that Layla is obsessed with Cecil). After all, Layla is the heroine of a yandere otome game.
4. Layla is a pervert, and always was. The only reason she wasn't one in the game is because of the player's direct involvement.