I did a couple of the original DS, and it wasn't that bad, but there are definitely two things to keep in mind:
1) Make sure that you keep each type of screw separated, and do not lose any. They are small so you will need to make sure you put them in something so they don't roll around while you're working.
2) When taking it apart and putting it back together, be careful with the cables that connect the bottom and top sections of the DS. They will be inside the hinge in the middle, and they can become damaged if you aren't careful.
Keeping these things in mind you should be okay. I would imagine that the DS Lite has lees room to work with when replacing the case, but if you take your time and take care not to damage the parts, you should be fine.
A quick google search for "replace ds lite case" (without quotes), provides a great variety of instructions on the first page, take your pick for whichever is the most understandable for you. Whatever you choose, I wish the best of luck to you.