You can try a number of things.
1) larger water bowl
2) move water bowl under the lamp
3) instead of using cardboard, you can use tin foil, damp towel, or plexiglass. Cardboard doesn't hold moisture well.
Lamps suck the humidity out like a sponge so they're not recommended unless there's not any other way to keep your temps up. Do you have a heating pad?
You can also make a humid hide for him.