How to find the secret exit on level 15, Spawning Vats, and
get to level 55, Fortress of Mystery:

First, look on your Automap.  The level's entrance is along
the northeast corner/edge of the map.  Use this room as the
starting point of reference for the instructions.

Walk out of this room and curve around to your right, and
head north, past a door on your left, and continue around
west, walking past a mural of the head of a Baron of Hell.
Follow the path around and head south, passing an open
doorway on your right, and approach a room to the south
with a shallow lava pit at its center.
Walk into this room and look for a wide passage to your
right.  Take this path and follow it east into an area of
brown cobblestone floors, and take your first right, south,
into a roofless rectangular chamber, with 3 green
"closet"-like structures recessed into the wall ahead of
you, to the south.  (There are also 2 more closets in each
of the walls to your left and right... these can be ignored
for the moment.)
Of the 3 closets on the south wall, step into the center
one, and you will be teleported to a tiny, separate chamber
in the southwest corner of the map.
Ahead, you'll see a face-like switch (or a doorway) across
a short stretch of lava.
Run all the way across the lava, and up into the doorway.
(This triggers an event back in the "green-closets" room.)
Quickly reverse and run back to the other end of this
chamber.  You'll teleport back to the green-closets room.
You'll have your back to the center closet, and you'll be
facing north, towards the room's entrance.
Immediately turn right, take a step or two, and turn right
again to look into the next closet over (the one in the
southeast corner of the room).
You should see a skull switch, behind a panel which is only
temporarily raised.  (If you were fast enough, the panel is
still up.)
Step up to the skull switch in the closet and activate it.
Now you're off to level 55, Fortress of Mystery.