>>35511882version for all the wind haters.
The Psychic type on Lugia has always been questionable on every level:
--for one thing, the 3 Psychic moves it learns, are moves Ho-oh learns as well
--all the lore and info about Lugia talks about concepts like storms, weather, the ocean.. while not mentioning anything that would somehow explain the Psychic type.
--on top of that, not just is it odd to be Psychic-type, for some reason, Psychic is even supposed to be its primary type despite Aeroblast being its signature move.
I honestly wouldn't be surprised if they didn't really give it much thought back then, and the explanation turned out to be that it is just a leftover from these legendaries data being that of a recycled Mewtwo as the base (as is evident by looking at the stat distribution).
My retcon suggestion may look weird with Flying being in different roles for them individually, but that's because that is exactly the case conceptually.
In Lugias case, the Flying type is intended to represent the storm/wind aspects. So Flying would be its Element so to speak, being its counterpart to Ho-ohs Fire type (Which would fit with how their signature moves are Aeroblast/SacredFire respectively)
In Ho-ohs case, the Flying part is not representing an elemental aspect, but the simple practical ability of flight that is natural to birds.
And with that in mind, it would make perfect sense that Lugias match to Ho-ohs literal Flying type would be the Water type, to showcase it being "the Diving Pokémon" that lives on the bottom of the ocean.