To reach the exit door on Doom level DEIMOS LAB:

The exit door is located high up on one wall of a lava pit
at the southeast corner of the level.

(To get to the pit, first go to the very large, circular
room in the northwest quadrant of the map.  At the core of
this large circular room is a smaller central chamber.
Note that in the PC version of this map, a switch-activated
staircase leads up to that small chamber; but in some other
console/handheld versions of this map, there are no stairs.
Inside that central core chamber is a small, raised, square
platform.  Walk across it, and a wall will open up in the
south side of the larger circular room, revealing a hallway
leading south.  Go down that new hallway and step into the
teleporter booth at the far end.  You'll materialize at
another teleporter near the southeast corner of the map.
Turn right and walk south until you come to the lava pit.)

Once you're at the edge of the lava pit, look left (east),
and you'll see the exit door, high up on the east wall.
Just below and to the left of that exit door is a narrow
booth with a solid floor.  Jump down into the lava and Run
into that booth.
Activate the switch on the south wall of that booth.  This
raises a bridge that leads from the north edge of the pit
to the exit door.
Once you activate that switch, turn around and step on the
teleport pad you'll find there.  You'll materialize on
another teleporter near the center of the map.  Step off
that teleporter, then step back on again.
Turn right and walk back to the edge of the lava pit.  From
there you can walk across the bridge to the exit door.

PC Doom players can access a demo of this level that shows
how to get to the exit by clicking here.

Hope this helps. :)                                                              

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