Lugia is pretty tough and he’s one of the stronger Pokemon out there, but he doesn’t stand a chance against Greymon. Greymon has his Nova Blast after all! One good hit is enough to take down just about anybody. Even if Lugia could survive it, I don’t think he could endure a Terra Force attack! It would just be too much for him. Greymon wins.
DReager1.com 
Assuming Lugia hasn’t been captured by a Pokéball before the battle, I’d give this one to Lugia.
True, if he were in a Pokeball, I don’t think that he’d have a shot. Well, I’d take Lugia over a Greymon any day, but thanks to composite rules, Greymon has his Double Mega form. That may prove to be too much for Lugia this time.