If the screen accepts VGA, you can use GCVideo lite (clone of component cable) and set it to RGB mode. After that, just wire Red, Green, Blue, H-Sync, and V-Sync to the correct input pins on the screen.
Many LCDs don't support 15KHz VGA at 240p/288p and 480/576i so you may have trouble with games that do not support 480p. The BIOS is 480i so that won't display either.
Which GC revision are you using? DOL-001 or DOL-101? I ask this because the DOL-101 requires a couple more parts to enable 480p support.