grass
dragon and ice type pokemon
FIRE ELECTRIC PSYCHIC
Ice, Rock, and Electric are super affective against flying type
Ice and dragon
Tackle.
Ice moves, Water moves, Electric moves, Rock moves.
Since Lugia is a Psychic/Flying type pokemon, I would try Ghost types and electric types. Ice types are also a good choice
Your Pokemon should be around levels 32 or higher and use super effective moves on her Pokemon as well like fire, flying, ice and poison are really affective they do 2x damage.
ice/snow types
The best Pokemon to have in Pokemon diamond is Arceus because he has the best stats in Pokemon diamond. Answer 2 Marowak and Latios are better. Answer 3 Dragonite would have to be the best! It has great stats, is immune to a lot of types and can learn many moves like fire-type moves to deal with super effective ice-types.
The ice rock is found on route 216.
Fire and steel types are super effective against Ice Pokemon. Electric, although super effective against water, do only normal damage to Ice Pokemon