Lugia

Dragon Tail+Sky Attack and Future Sight

With its 3 DPT (Damage Per Turn) and 3.33 EPT (Energy Per Turn), Dragon Tail is Lugia's best quick move due to its solid power and extremely wide coverage. Sky Attack (80 Power/45 Energy) comes out surprisingly quickly, especially considering the higher than average energy gain of Dragon Tail, and hits fairly hard. Sky Attack is an absolute staple on Lugia as it grants good coverage, good power, and allows it to act as a shield-shredder to a certain degree. It also has access to Future Sight (120 Power/65 Energy), another decently fast charging and fairly powerful attack to act as a mini-nuke when coming off of Lugia's STAB. This set functions in a manner that allows it to act as a quasi-lead and a quasi-closer, perfectly complimenting Lugia's play-style as the great wall.

Dragon Tail+Sky Attack and Hydro Pump

This set is virtually the same as the one above, but it sacrifices a bit of power from Future Sight to instead gain coverage from Hydro Pump (130 Power/75 Energy). Hydro Pump takes longer to charge, has lower base damage per energy, and lacks STAB, but it does allow Lugia to perform better against a number of potential threats. It can hit Tyranitar for super effective damage while dealing at least neutral damage to other threats such as Metagross and Melmetal, who otherwise wall Lugia with their resistances. It also allows Lugia to directly counter Groudon in a fantastic way, making it the moveset of choice if your team doesn't appreciate facing the Continent pokemon and its unique, earth-moving skills. In short, this moveset is more focused as to fill team holes, while the previous moveset is more for running Lugia on its own merits and building a team around it.