You can find the factory manual at
http://www.hondahookup.com/manuals/USDM_92-95_civic.zip

Assuming it is a 4 door (the 3 door didn't come in LX trim, don't think
the 2 door did either) there are the three screw you have found:

1. The screw that hold the door lever. After you unscrew it, you need to
unhook the handle rod. It is held in place with a plastic clip that you
swing out of the way.

2. The screw at the bottom of the arm rest pocket. Unscrew and remove
pocket.

3. The screw at the upper front part of the door. Unscrew and pry out
the plastic plug it is screwed into.

Then the panel is held in place by a number of plastic clips along the
front, bottom and rear edges of the door. You can use a trim pad remover
for this, but in my experience it is easier by hand. Get your fingers
under the panel and pry it out, getting your fingers as close to the
clips as possible. Do this around all three edges. On the 2 / 3 door
models, one of the bosses holding the plastic clip (second from the top
along the rear edge) breaks easily, not sure if this is the case with
the 4 door. If one breaks, it is of little consequence.

Then get various grommets, switches and connectors out of the way and
lift the panel straight up to unhook it from the top edge of the door.
Then remove.