Amity wishes she could spend more time with Luz, one of the few comforting presences in her otherwise difficult life. But outside of a handful of classes or lunches, they barely see each other.
So when Gus makes an illusion of Luz to help her juggle a conflict between tracks, it's no wonder Amity is eager to take it home with her. At first she tells herself it's just to practice asking Luz out, but before long she starts spending more and more time with it, risking losing sight of reality as she becomes enamored with the illusory Luz.
Amity wants to tell Luz how she feels about her, but only when she has a chance to plan it out and get the words exactly right.
But when Luz gives Amity an especially thoughtful gift, Amity, overcome with emotion, impulsively kisses Luz on the cheek. Mortified, Amity runs away, leaving a confused Luz to try to make sense of how she feels about her friend while Amity tries to salvage what she sees as a disaster, but everything she tries seems to just make things worse.