In regards to the topic, yes, Lugia is indeed a Legendary. Just because it breeds does not mean it is not a legendary. it was made quite clear in all pokemon media that it is indeed a legendary. Also, Off topic but to Smarties-kun:
Any post that uses the anime as back-up has the words 'Fail' printed on it in huge red letters. ._. The anime does not only contradict the manga and games, but it also contradicts itself in more ways I can bother to count. The manga and games, however, don't contradict each other, which definitely makes the anime the odd man out.
Ummm... no offense, but about the Anime being the only Pokemon media to contradict itself or any other Pokemon media, the games kind of contradict themselves as well. For evidence for the games contradicting themselves,
1. The Mew entry in the researcher diary on cinnabar island stated that it gave BIRTH to Mewtwo, and yet the pokedex entry for Mewtwo said that it was more or less the result of a gene-splicing experiment, and gave absolutely no hint that it was the offspring of Mew.
2. The Pokedex entries stated that Marowak gave childbirth and dies as a result, and yet when you breed a Marowak, not only does it live after breeding, but it lays an egg.
3. Cubone's Pokedex entry states that it's skull helmet came from the remains of it's dead mom (Marowak), and yet when a cubone hatches, it also seems to be born with the skull helmet latched onto it's head.
4. Vulpix's pokedex entry stated that it was born pale and with a single tail, but when hatched from the egg, it has it's 6 tails and its normal coat.
5. Kadabra's pokedex entry hints that it was originally a human being, however, from the multitudes of Kadabra (not to mention that it can evolve into another pokemon [Alakazam], and breed to create it's pre-evo [Abra].) it doesn't really seem to be the case.
6. Mew was called the ancestor of all pokemon even in Diamond and Pearl, and yet they mentioned Arceus being the creator of all pokemon.
7. And not to mention the multitudes of legendaries despite them being genderless and one of a kind (Emerald battle frontier, anyone? or how about the Colosseum/XD games? or how about FR/LG [there is the part where Entei/Raikou/Suicune are running around Kanto despite the fact that the 3 beasts are not supposed to awake for another 3 years.]?)
I can't really say the same for the manga, but they did state that Misty was some rich lady in one manga, and yet was not mentioned to be that in the games, plus, they made some of the gym leaders rocket members (or ex rocket members, in Blane's case), when, with the exception of Giovanni, it wasn't the case at all in the games.