Since Lugia is a Psychic/Flying type pokemon, I would try Ghost types and electric types. Ice types are also a good choice
Water Type is super affective against claydol
Poison and Fighting.
Ground types
water, fighting,
Grass is super affective against whiscash it might be *4 instead of *2 attack,
Water Type is super affective against claydol
Lugia because it is physic and super affective against poison and fighting but don't use it against dark because they will kill it easily
Fighting-type
ghost
Electric type
psychic
Poison and Fighting.
Ground types
water, fighting,
Dark, Ghost and Bug.
Grass is super affective against whiscash it might be *4 instead of *2 attack,
Dragon-type moves are super effective against Dragon-type Pokemon.