Well since its been verified that after you find legendary bird that is linked to your starter multiple times, it flees to this Den. The following is speculation based off Regigigas. Since for Diamond and Pearl, we had to transfer the original 3 regis to get to Regigigas; I'm thinking the same for lugia if its programmed into the game. If someone brings all three legendary birds (original 3) to the den, perhaps lugia may appear in a special event?
A similar event happened for Rayquaza when kyogre and groudon were brought to a special location in heartgold/soulsilver.