Here's why:
* Shiny Pokémon were not introduced until Generation II: Pokémon Crystal is a Generation II game, and the Shiny Pokémon mechanic was not implemented until Generation II.
* Lugia is not available in the wild: Lugia is a legendary Pokémon that can only be caught in a specific event in Pokémon Crystal. This event doesn't involve encountering Lugia in the wild, so you wouldn't be able to encounter a Shiny version.
While you can't find a shiny Lugia naturally in Pokémon Crystal, you might be able to transfer one from a later generation game where shiny Pokémon are available.