Check turn signals, cornering lamps, four bulbs in trunk lid (two per side)between back-up lights and edges, back-up lights, as well as head, parking, and tail and brake lights. Any of these will will trip the 'check external lighting' message. I don't know for sure if the license plate light or the third brake light will cause this but my guess is that they are included as well. Actually eyeball the lights yourself. Don't depend on looking for light reflecting off objects to determine if light works. Example: Putting car in reverse and looking for light on a building or car behind you won't tell you if both back-up lights are working. From the pictures it appears that you have HID housings in the front. I don't know if LSCs were available with halogen lights. Maybe some one else can enlighten us on that matter. Try this: determine if you have HID or halogen headlights. Not trying to be a wise guy, but if you don't know how to tell the difference, ask we'll tell you. Turn on headlights, turn on high beams. If your car has halogen low beams, they should turn off when you turn on high beams. If you have HID low beams, they should stay on when you turn on high beams. If your car was originally equipped with halogens and converted to HIDs, you made need a little work on the wiring.
If all else fails, contact the previous owner and ask him about the lights. any work done on them or problems with them he knew about. SUGGESTION: if you contact previous owner, speak in pleasant tones, tell him how much you love the car, then ask him about the lights.
Hope this helps.
Bill