The Underground Lair is a location under the Cathedral.
Two had left the orphans in the Underground Lair where they'd be safe until she returns from her missions. Cent had given the soldier Two's power in order to protect them. However, the magic backfired and all the soldiers in the Cathedral had become enhanced soldiers. The children in the Lair had all merged into the Homunculus. Two and Cent here forced to kill the beast which lead to Two losing her mind.
In Branch C, Zero arrives in the Underground Lair where she finds One sitting in wait with her Deamon, Abdiel. Upon Zero and Mikhail defeating the Golem trio, they opening portal to summon Gabriel. Mikhail sacrifices himself to kill One's dragon, leaving Zero to fight One alone. After kill One, Zero limps her way out of the Lair in search of another dragon, vomiting as she walks.