To unlock the dungeon, go to the high school and talk to a girl in front of Classroom 1-2. Then, speak with a girl at the practice building. Next, talk to a cop at the north end of the shopping district near Konishi Liquors; he is available on Mondays, Wednesdays and Fridays. Later, talk to Chie at the Samegawa Flood Plain Riverbed, and then talk to the cop again, who reveals Naoto's "obsession" towards the cases. Next, speak with the housewife standing in front of the Tatsuhime Shrine, and go to the shopping district South on Tuesdays, Thursdays and Saturdays to speak with a cop who talks about Naoto being "treated like a child." With these two clues, the dungeon's location is revealed.
The Secret Laboratory is different from the other dungeons in that the floors descend, ending at the bottom. As the Team continues downwards they are given warnings to turn back. Rise interprets this as Naoto's refusal to mix with other people. On the sixth basement floor, the Team is stopped by a locked door requiring the Leader Card. The Team explores the dungeon to find the Research Card (in a treasure chest), and goes back a few floors until they find a locked door on the fourth basement floor. This leads to a Boss guarding the Leader Card.
After successfully defeating the "Dominating Machine," the Team continues on until the final basement where they find Naoto confronting her other self. The "Other Naoto" spells out everything, most surprisingly the fact that Naoto is, in fact, not male. Naoto refuses to accept her other self and a fight against her shadow commences. Later, Naoto realizes that everyone must accept his or her true self and continue on with life, regardless of their appearance or personality.
This concludes their rescue, but Naoto's words before succumbing to fatigue are sound and true; the case is far from over.
In the Persona 4 The Animation, the Secret Laboratory is destroyed by Beelzebub's Megidolaon.
After entering Secret Laboratory, one of the dialogue choices is "I do not comprehend" which is the catchphrase of Gale from the Digital Devil Saga series.
The text on the hologram projectors of the Secret Laboratory is actually from a French Huffington Post article about a Japanese Agricultural Minister who resigned.
Edit
