Psychic: represents space and things in space (like the moon). It's the type the main legendary trio of Sun and Moon (Solgaleo, Lunala and Necrozma) share.
Ghost: Lunala is a bat. Alola is based off of Hawaii. There are two native Hawaiian species of bat, one of which is the extinct Synemporion, or the ghost bat. It's also based off of Camazotz, a Mayan bat god that was associated with the night, death, and sacrifice.
Lunala's design origins