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Dragon and Ice types are super effective.
There is no TM Dragon Drance
It may sound weird but the only types weak against dragon Pokemon are other dragon Pokemon except ice types for some reason.
Dragon and ice types defeats it
well you come across a whole range of pokemon from rock to ghost types. The boss has a tough collection of dragon types so i think you should take a variety of pokemon, if you have already caught Lugia this would be an advantage, especially if it's a high lvl pokemon.