The Fowl Lair is a small dungeon that is a possible outcome of the Ancient Device in Act II of Diablo III.
Just like its name suggests, the dungeon is filled with fowls (chickens) that the player cannot interact with: they just wander around and gobble.
At the end of the dungeon, there is one killable Greasy Pig. Upon death, it drops loot as if opening a Resplendent Chest.
Name of the dungeon is, most likely, a pun towards the "Foul Lair".