Poor Luna seriously doesn't get to keep any of her most treasured items out in the open:
He grabbed another stack of printouts that he'd set aside on his treasure chest. That's what he called it—the locked steamer trunk that contained his life. His desired life. The girl clothes. The makeup. He'd even wired the trunk with an alarm system. (8.105)
Because Luna is hiding her true self from the world, she has to keep all her girl things in a locked steamer trunk. This is symbolic because she has to guard herself carefully, showing Liam to the world and not letting Luna come out. Especially around her father, she must always keep her makeup chest—her true self—hidden.