Often use Mewtwo and Lugia in a pair. Using them means either:
#1: Countering something that is weak to Psychic and/or Flying
#2: Battling against something that is Psychic-type
#3: I need generalist power because I am lacking in high-DPS specialized counters.
They make a great pair, especially since Mewtwo is relatively glassy and Lugia more than makes up for that. Lugia is a great choice for the last slot of a team because it is easy to dodge with, super tanky, has decent damage, and can quickly get off a Charged Move which is valuable for the "overkill" damage bonus in raids.