Level 1:
* Gust (Flying)
Level 5:
* Screech (Normal)
Level 11:
* Extrasensory (Psychic)
Level 17:
* Aeroblast (Flying)
Level 23:
* Ancient Power (Rock)
Level 29:
* Mirror Coat (Psychic)
Level 35:
* Psycho Cut (Psychic)
Level 41:
* Sky Attack (Flying)
Level 47:
* Ice Beam (Ice)
Level 53:
* Thunderbolt (Electric)
Level 59:
* Outrage (Dragon)
Level 65:
* Hydro Pump (Water)
Level 71:
* Aeroblast (Flying)
Level 77:
* Hydro Pump (Water)
Level 83:
* Aeroblast (Flying)
Level 89:
* Hydro Pump (Water)
Level 95:
* Aeroblast (Flying)
Lugia also learns the following moves by TM:
* Toxic (Poison)
* Thunder (Electric)
* Earthquake (Ground)
* Blizzard (Ice)
* Brick Break (Fighting)
* Psychic (Psychic)
* Shadow Ball (Ghost)
* Hidden Power (Normal)
* Rest (Psychic)
* Substitute (Normal)
* Protect (Normal)
* Return (Normal)
* Frustration (Normal)
* Solarbeam (Grass)
* Flash (Normal)
* Double-Edge (Normal)
* Reflect (Psychic)
* Light Screen (Psychic)
* Safeguard (Normal)
* Amnesia (Psychic)
Remember that you can also teach Lugia moves by using TMs and HMs, so you can further customize its moveset.