Water, where oysters, and thus pearls, come from. Also putting work in the theory that Dialga, Palkia and Giratina are connected by the 3 states of matter (Dialga : Solid, steel type ; Palkia : Liquid, water type ; Giratina : Gas, ghost type).

I ain't got jack for Lugia though.

Psychic was just the go to for a lot of legendaries, it was the "mystic" type.

Lugia is known more for the weather itself than direct control over water… but seeing how it's the guardian of the seas… water typing might have been appropriate. Hell, dragon would have been cool… but this is passable I guess.