I wouldn't call them "opposites". They both have a peaceful co-existence. They don't have to be banished to opposite sides of the world to avoid having some huge battle, unlike some other legendaries. They used to live atop the Brass and Tin towers, and never once tried to fight each other. :\ So the whole "Water vs. Fire" thing seems irrelevant to me, since there's not one good reason for them to ever battle.
As said, Lugia aren't naturally from the sea. They have incredible powers that could accidentally cause horrible destruction, so they hide deep in the depths to protect others from being affected by them. Lugia doesn't seem to have any "powers" over water, like, say, Kyogre. They can calm and create storms, but that's more of an atmospheric thing than a strictly water-based ability. It presumably got the "Guardian of the Sea" title after it fled Ecruteak City, and started living in the sea. I think it only lives there because it's the only place it can't do any harm.
Then there's the whole telepathically speaking thing, which, as has been said, is usually considered a Psychic-type power.
There's another thing that could be possible. They have incredibly strong power. This "power" isn't water-specific at all. Psychic types are shown to be very powerful and mysterious. All the psychic types at that time had some special, unnatural power. Mew, Unown, Xatu, Espeon, Wobbuffet... the list goes on. I think it could be purely because Psychic is just more interesting. I mean, it could be in the same class of pokemon that can... swim and squirt water out of their mouths, OR, it could be in with the group that can create invisible walls to block attacks, see the future, eat dreams, teleport, reflect attacks back at the user at twice the power, and travel between dimensions. If I had to choose between placing it into one of those two types of pokemon, I think the choice is obvious.
