Lunala is Psychic-Ghost type for the same reason Solgaleo is Psychic-Steel
>in pokémon the psychic type is usally give to cosmic pokemon for the relation of ESP powers and paranormal stuff, Solgaleo and Lunala are pokemon that represent the Sun and the Moon and travel across the space between timelines, making psychic type the perfect type for them
>in alchemy, the green lion that devours the sun represents the life growning thanks to Sun's light (in this case the green color represent plants) and the purity of metal, because once you apply sulfuric acid to metals (green color representing said acid in this case) the lesser ones are destroyed, while the pure metal of gold (represented by the Sun) resist impassible, this makes Solgaleo, the alchemic lion of life, Steel type
>like wise, the decomposition of lesser metals and the death are represented by the skeleton in alchemy, which is why Solgaleo's counterpart, the lunar bat Lunala is a Ghost type skeleton
>other details of the line are also based on alchemy, Cosmog is pure Psychic type because it still fits the cosmic pokémon cuota by being a nebula (same for Cosmoem, who is a proto-star), and this also coincides with one of the steps for the transmutation of the Philosopher Stone (quoting the Emerald Table: "The Sun is its father, the Moon its mother, the wind hath carried it in its belly, the Earth is its nurse.") since Cosmog is a ball of gas born from a male Sun and a female Moon (Sun and Moon's genders in alchemy) that come from the space, but is still raised on Earth until it grows enough to left the world and travel across the ultraspace on its own
>this connection with the Philosopher Stone is why the Pokédex mentions Solgaleo is believed to be male and Lunala female, and also why their shiny forms are crimson red
