Its difficult to tell from the picture but it looks like the desk may be MDF with a picture finish. (Meaning it is wood fibers mixed with glue and pressed to make a board. It is then covered with a plastic-like picture of wood grain.) If that is true there isn't much you can do to repair it. MDF swells when it gets wet and it is almost impossible to get a flat, smooth surface again.

This is an old question but I thought I'd answer since its an easy fix. It looks like you have a machine screw going into a wooden knob. (There may have been in insert that was lost over the years.) I think the easiest fix is to get a replacement wood screw. If you take the lid and knob to your local hardware store they will be happy to show you what you need.

Apparently LED light strands are different from the old style I'm used to. On LEDs you have to make sure the polarity stays the same when you replace a bulb or the current is reduced and the lights dim. Pay attention to how the bulb/holder was in the wire and put it back the same way. Also, if the bulb happens to lose one side of the tiny wire inside the holder that is plugged into the strand, the strand will dim.