As I see it, the Birds all represent a season (Winter, Spring and Summer), which Lugia has little to do with. However, Lugia is related to the Moon, which is also related to tides (Also related to the sea, and by extension, Lugia). These affect the world and the weather, bringing changes in several aspects. Seeing how Lugia can cause the Great Flood when it flaps its wings, which has to do with weather somewhat, but more with wind than with rain itself (Which is the case for Kyogre), I can see a slight connection with the seasons the Birds seem to represent. Something I hope they finally ellaborate upon.There's no clear relationship between these in the games... besides XD. Greevil uses not only Shadow Lugia, but also Articuno, Zapdos and Moltres. Yes, this was most likely made to have more Pokémon available, but seeing how you needed LG to obtain all Pokémon not found in Emerald anyway (Due to the Starters, the Fossils and Slowpoke), they didn't need to put them in at all. Yet they did, and I always thought that had to mean something. More so, they're all under ownership of Cipher's Boss. One individual. Not spread, but all commanded by him. Of course, most people think these "Spin-Offs" are still unrelated to the main series, so yes. This is just how I see things...
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