LED technology is pretty advanced now. They have really really super duper bright LEDS now.
Afew years ago i made an LED system for my room, it was pretty cheap and was quite phsycodelic.
what you do, is get some cable trunking from BandQ. This is a long plastic gutter with a snap on cover to hide cables. Make sure you get one that dosnt have sticky pads on the back.
Using a very small drill or a needle or something, poke holes for all your LEDs in the back of the trunking. Push the LED legs through, adding a blob of CA gel or super glue. Make sure you get the polarity round the right way (meaning all the positive legs (the long ones) are all on the same side) now you just bend the legs out inside the trunking, then start at o ne end working down and solder a copper wire onto each leg. You can light them with a 12 or 9v transformer, just make sure you get one meaty enough for all your LEDs.
Snap the top back on, and put sticky pads or screws into it to fix it to the inside of the lid.
It will cost you about 20 quid all in all....