Lugia

As a cover legendary, Lugia is somewhat disappointing like Ho-Oh. Its stats are heavily slanted towards defense, which is not ideal in raids. Because it is a legendary species, Lugia can’t use its bulk as a gym defender, so its role is primarily as a bulky Psychic/Flying-type attacker. Unfortunately, Lugia often finds itself outclassed despite Aeroblast's incredible damage, as many other Psychic or Flying attackers have significantly higher Attack. Its lack of Flying-type fast move further limits its potential.

Apex Purified Lugia wields the obscenely powerful Aeroblast++, the strongest charge move in the game. This somewhat makes up for Lugia's low Attack stat and raises its DPS to respectable levels. However, its Shadow form is the real deal, and it is not recommended to purify Apex Shadow Lugia if you care about its raid performance.

Best PvE Offensive Moveset

• Extrasensory is Lugia’s best quick move, targeting Poison and Fighting-types for STAB effective damage.

• Dragon Tail can provide neutral coverage against Psychic-types.

• Future Sight isn't a bad move and has the advantage of pairing with Extrasensory, but in most cases it's best to use a Flying Type option instead.

• Sky Attack is an outstanding attack, but for sheer Flying Type damage, Aeroblast is better.

• Aeroblast++ is an even stronger version of Aeroblast, but it is exclusive to Apex Purified Lugia

• Hydro Pump isn’t a bad charge move, but it has no use on Lugia.

With the Season 8 buff to Dragon Tail, its incredible damage output now makes it the superior option to Extrasensory despite having slightly less energy gain. Dragon Tail is especially preferred in Master League due to the ubiquitous use of Dragon-type Pokemon. 

Sky Attack is a very efficient move, benefits from STAB, and costs the least amount of energy. Future Sight requires a steep 65 energy cost, and is generally not preferable due to this cost unless Psychic-type coverage is highly needed. Hydro Pump (130 Power/75 Energy) 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, such as Steel- and Rock-types. The addition of Aeroblast from the Nov 2020 Animation Week event is a debatable but nonetheless welcome addition to Lugia's kit, demanding an expensive 75 energy cost but in return offering a massive 170 base power (2.267 DPE). With STAB, Aeroblast when resisted performs almost identically to Hydro Pump, which makes Lugia's signature move more preferable due to its minor chance to proc its +2 ATK buff, despite not offering additional coverage. 

Aeroblast++, the signature move of Apex Purified Lugia, is functionally identical to Aeroblast in PvP.