I've been trying to add a few custom icons to the lightboards, but I can't figure out how.

//-------------------------------------------------------------------------------
// This file specifies which icons are going to show up on the lightboard at the 
// beginning of the level if you need to add a new icon, you must add the actual 
// icon to the end of the texture sheet AND add it to g_pszLightboardIcons in 
// vgui_mp_lobby_screen
//-------------------------------------------------------------------------------

It seemed simple enough, and adding the new icons to the texture sheet was trivial, but I can't find vgui_mp_lobby_screen anywhere. In another thread, someone mentioned using vgui_level_placard_display entities to do this, although I wouldn't know how to use them to do this.

I would prefer not to use Omnicoder's Chamber Sign Maker (although it is a great program), so I would really appreciate any help.

Probably have to use a custom texture.

Start here: community-releases/chamber-sign-maker-t2797.html

I was looking for that too. It's probably some kind of editor script which was not necessary to make downloadable with Portal. The only mention of that name are in the comments at the start of the lightboard icon files (coop_lightboard_icons, sp_lightboard_icons, lightboard_startup_sequences).

The only way to manually change this using the lightboard vgui, would be to replace Valve's icons temporarily with yours, perhaps using a .vpk. I'm not sure if this will replace any default textures, especially ones that are loaded with the lightboard signs.
For example replace the icons you know you aren't going to use on your sign with the 'same named' custom icons by using a .vpk.

Wouldn't it be easier to create a custom texture and fake the lightbox? otherwise your gonna spend a big amount of time on something people look at for a second or two...

Anyways, you could try Omnicoder's Chamber Sign Maker

And here is another tutorial(+video) on how to fake the lightbox...the end result isn't bad and could easily be improved and modified to fit your needs.

But I do gotta admit, the script system that Valve put in is really cool.Its a shame no one installs it because they fear breakage of the retail game.

In most cases, a sign texture is best, since you need to add custom icons. I looked into doing it via script, and I think all the icons are hard coded.