I thought Legendaries generally couldn't reproduce...
Like what @gojiramon said, presense of a baby Lugia hints at reproduction. Now, personally, I think that they CAN reproduce because generally speaking, all creatures that are not fungi or plant-like have a male and a female sex, necesitating the finding of mates. And since Pokémon are essentially creatures, then they can reproduce, especially those who are mammalian in appearance/association.
One theory on why Legendarys cannot seem to reproduce, can because THEY ARE SO RARE. Thoughout the ages of human hunting, war, natural changes, lack of finding good mates or even just the sinple passage of time themselves are all reasons why the Legendaries have hardly any offspring.
Further reasoning why Legendaries cna reproduce is that a Black Shiny Rayquaza appears in of the films, the Legend of Hoopa, implying that there are other Rayquazas that are mostly green, and that some Rayquazas turn black-colored.
As for why Legendaries have no gender in the games....that simply as the developers not wanting Legendarys to be bred, from a game play standpoint. But one explanation for that could be that Legendaries sinply cannot breed with other Pokémon; they must bred only with another of their kind. Another explanation could be that Legendaries are genetic mutations of "regular Pokémon" are therefore cannot exactly reproduce...sort of like how mules, the offspring of a male donkey and female horse, cannot reproduce themselves.
Like what @gojiramon said, presense of a baby Lugia hints at reproduction. Now, personally, I think that they CAN reproduce because generally speaking, all creatures that are not fungi or plant-like have a male and a female sex, necesitating the finding of mates. And since Pokémon are essentially creatures, then they can reproduce, especially those who are mammalian in appearance/association. (...)
Mostly agreed on the general points, but... fungi and plants also have sexes. Though plants mostly have both while fungi are... complicated.
Speaking of, maybe Legendaries just undergo binary fission or budding or just abiogenerate spontaneously as manifestations of nature and other concepts. Sort of like how elemental spirits and personified concepts do in real-life mythology/folklore.
