My question is just the title. I usually leave the front half of the lid off because it's such a pain sliding it on and off every time, especially since it sticks a lot.(I leave the back one on to support my lights. I'm working on a way to make it so my uvb gets through the mesh.) The only reason I can think of to put it on is if the beardie is trying to get out, but Bodhi has never tried anything like that.(She seems to enjoy her tank more that outside.)
If there aren't any other animals around to try and get in you don't really need the top. I leave the top off of my tank and it's not a problem. The lights are able to reach into the tank really well without the mesh in the way. I just suspend everything above the tank.