Little is known about these powerful, deeply intelligent and majestic beasts of the sea: they are an exceptionally rare sighting beyond certain areas and even in those areas they only rarely appear near the surface. However, the partial data we do have suggests some fascinating possibilities.
Lugia exhibit many conflicting traits - great muscle mass (allowing them to tirelessly fly or swim) alongside light yet extremely strong bones, capable of withstanding massive pressure. Their bodies are covered with a a thick layer of insulating, water-resistant plumage of a silvery color (these have come to carry some spiritual significance to certain island populations) and yet their wings aren't on the whole particularily avian - being more similar to chiropterid wings with very thick membranes or even to human hands, complete with one 'opposable' digit. These wings appear to serve as flippers underwater, allowing some very rapid propulsion through water as well as through air.
Lugia spend most of their time deep in underwater trenches. They seem to be adapted for deep dives, and it has been theorized that the adults at least have some form of limited underwater breathing capabilities. This makes them exceptionally difficult to observe, and as such we know very little about their diet (though we presume they are carnivorous due to their sharp teeth and the bony growths on the side of their 'beaks') or social structure (though we know they travel in pods in a manner similar to cetaceans when caring for young, who may be unable to dive for the longer periods of time the adults can). Telepathy may have a part to play in their communication, though they appear to primarily commune through intricate vocalizations similar to whalesong. Lugia vocalizations have been recorded before, though humanity is still far from decoding their intricacies.
We do, however, know that Lugia have a large and highly developed brain - and they have been observed displaying psychic capabilities, including some form of localized weather control - on which they are said to have a balancing effect of sorts. That is not to say that such is always the case: Lugia are capable of causing massive storms by beating their wings - and legends say that one of the reasons to their underwater reclusiveness is their awareness of their own power, which may conflict with their legendary role as guardians of balance.