With a fluorescent light strip I would get a glass lid and put the light on top. The lid will help prevent evaporation...most any acrylic or glass strip can work. You really only need a lid large enough to protect the light.
No they don't have Eye lids . What they have is a thin membrane that comes down over the eye to protect it when they are in attack mode or about to bite something. Its not a voluntary movement like we have though.