It's time to go to the Moon, fly your airship to the Lunar Whale, get inside and talk to the crystal in the middle it'll take you directly to the Moon.

Go to Hummingway Abode which is located at north of the map.

Inside you'll Level Lust augment and an Eidolon. Just go and greet him for your side quest. There is also a shop here who sell a unique item Siren which we'll thousands of them when we reach farming section.