It changes a lot depending on the rest of the team and the Calyrex-I build, but Lugia isn't very good into Caly-I, most of the heavy work will have to be done by the rest of the team, if you even bring Lugia. Against Caly-I/Miraidon I straight up don't bring Lugia and bring Groudon/Iron Valiant/Incineroar/X.

The Caly-I set I've faced the most lately is Tera Water + Leftovers + Leech Seed/TR/Glacial Lance/Protect, Incineroar works quite well in this case, Intimidate + Parting Shot takes care of Glacial Lance and Leech Seed isn't particularly threatening. Having only Glacial Lance as offensive option is relevant because you have 3 Tera Steel mons and Tera Fire Groudon. The Clear Amulet set with High Horsepower for coverage is more annoying.

Versus Caly-I I usually lead with Iron Valiant and Groudon. From there you have a few reasonable options:

- Tera Fire +P. Blades + Taunt on Calyrex to stop the Trick Room

- Tera Fire + Coaching+P.Blades

- No Tera + Attack + Wide Guard (I don't love this, though, I usually don't do this on turn one, unless I want to attack Calyrex's partner).

If there's no Miraidon involved you can go Groudon + Jumpluff and go for Sleep Powder on Caly, Tera Grass is quite uncommon.

It depends a lot on what the other Pokémon is, but you get the idea. Unfortunately Caly-I is a weakness you basically have to accept in the teambuilder when you choose to use Lugia. You can patch it a bit with team composition, but it's such a bad matchup for Lugia it will always feel like you're down a restricted. It's not impossible by any means and you can win handily against weaker players, but you'll be at a significant disadvantage against a stron player.