General assumptions: Getting to the panic room in order to explore it is the last objective in the Penthouse stage. Locating the mentioned room is fortunately not too complicated.
If you didn't eliminate Layla in a direct duel, then you have to locate the panic room on your own. The room you're looking for is located in hardly accessible part of the penthouse. The fastest way to get there is the door in the room with the lift (screen above). You can unlock this door with a keycard (one of them can be found in Lenny's bedroom and another is in the room with a laptop) or wait until one of guards unlocks the door and sneak behind him.
You can approach a panic room also from the other side, crossing well guarded penthouse areas (a room with the whale skeleton among others). A room which is your target is shown on the above screen.
Start exploring the room. The entrance to the panic room is hidden in one of the walls (screen above).
Now you can start exploring the panic room. The only interesting item is a phone lying on the bed, shown on the above screen. Once you interact with it, the mission will be over.