gl engines don't use palette.lmp for actual rendering, its instead used only at load time.
this means they can't use the colourmap at all. they instead make assumptions about fullbrights and overbrights. the result is fairly close, but not identical.
colourmapping player skins can be emulated with basetex+toptex*topcolour+bottomtex*bottomcolour, which is only a 12-fold increase in memory usage compared to software rendering...

I know of only two engines that utilise the colourmap in opengl. one of them is my own, but it only uses it for regular world surfaces at this time. this results in banding of course, so its only desirable for people who prefer ultra faithful rendering. for anyone else its a bit more ugly.
3dfx cards used to support paletted textures. other hardware does not, as it pretty much makes blending impossible.
I don't have a clue what your 'colormap_palette.lmp' file is for, I've never heard of any such filename.
quake2 doesn't support lmp, but it does have a colormap.pcx file, the image data itself provides the colormap, while the pcx palette provides the palette for everything else (at least non-pcx content). I doubt its relevant, but its a vaugely interesting sidenote.
QW skins are strictly .pcx for ease of editing. the palette is not used. they are strictly 8bit for software rendering compat. if you want to make these work with dp (when not pretending to be a qw client), you'll need to split the image into three different versions according to the formula I gave in my first paragraph of this post. the 'base' texture should have the shirt+pants areas masked to black. the _shirt texture should have the non-shirt areas black, while the _pants texture (as a brit, that term makes me laugh) should have all but the nether regions masked black. the shirt and pants textures should both be greyscale, so that the player's colours can tint it accordingly.
.