Poison and Fighting.
FIRE ELECTRIC PSYCHIC
Ground types
dragon and ice type pokemon
Dragon-type moves are super effective against Dragon-type Pokemon.
Psychic Pokemon are Super effective by Bug type, Dark type and Ghost types
psychic
FIRE ELECTRIC PSYCHIC
ghost
Ground types
dragon and ice type pokemon
Dragon-type moves are super effective against Dragon-type Pokemon.
Ghost and psychic and bug type attacks
Psychic Pokemon are Super effective by Bug type, Dark type and Ghost types
Since Lugia is a Psychic/Flying type pokemon, I would try Ghost types and electric types. Ice types are also a good choice
Ghost Bug and Dark
It differs among card but generally speaking, psychic is weak against psychic themselves.
Water Type is super affective against claydol