The Lilith Mirror (リリスの鏡 Ririsu no Kagami) is an object allowing whoever holds it to see a monster's true form as well as their hidden desires, but at the cost of the user's soul.
The mirror was given to Kyoko by Ishigami with the intention to create a schoolwide uproar by revealing the students' true forms, but it eventually failed following Ishigami's defeat. In the anime, Kyoko accidentally obtains Lilith and the Lilith Mirror following a run-in with Kokoa, who was intending to use it to split Inner Moka from Outer Moka and keep Inner Moka for herself.