Shadow Lugia

Great League: 3 / 5

Thanks to its availability as a long-term research breakthrough reward, Lugia's CP can be low enough to enter into the Great League after a reroll of its IVs from a trade, and it definitely performs well here. Lugia can wall attack after attack while giving back decent punishment, and makes a fantastic team choice to cover a fighting weakness in particular. Notably, it absolutely dominates Medicham. It has the same flying-type weaknesses as other common Pokémon like Skarmory and Altaria. 

Ultra League: 3 / 5

Lugia's sheer defensive utility begins to shine through in the Ultra League, where it goes from a solid mon in a competitive Flying-type niche to a major threat. It holds its own against much of the tier, but its fatal drawback is its weakness to the masters of the tier: Giratina's two formes and Registeel. Regardless, with a bit of forethought, Lugia can perform very well in the Ultra League and support its team fantastically.

Master League: 4.5 / 5

Without the CP cap holding it down, Lugia gets to make use of its full power in the Master League. Possessing the game's highest bulk AND stat product, on top of a powerful moveset, Lugia is an absolute force to be reckoned with. Its typing and moves allow it to counter big threats such as Groudon, Palkia, Garchomp, and Focus Blast Mewtwo. Lugia's fantastic bulk also allows it to cushion blows from the numerous nukes in the metagame, making it an excellent Pokemon to catch charge moves with. The sheer power of Aeroblast can tear off a tremendous chunk of health even when resisted, making Pokemon like Dialga and Metagross seriously consider shielding it, while Lugia's bulk allows it to consistently satisfy the move's immense energy demands. Lugia is an excellent safe switch and, despite its many weaknesses, it pretty much only hard loses to Melmetal.