In The Lair level, get to the room where you see a Doom Artifact at the top of a huge pillar. To get the artifact, flick the skull switch behind you. 3 sets of stairs will appear. Walk up the middle set. Now turn left and you will see an area with a wooden floor. When you step on this floor, a switch will appear high on a wall near the pillar. Walk over to the window that overlooks the area and look around. If you don't see the switch you can try again.

Once you see it, shoot it and look in the small square window that slightly overlooks the stairs. Look through it and you will see another square window and another switch will be visible through it. Shoot the switch.

Now the Doom Artifact will be at ground level and will be ready for the taking.