I redesigned the base of this lamp to accommodate a wall-powered LED light. But it will also accommodate the battery powered ones from my other LED lamps. The wallpowered one is available here:

https://www.superbrightleds.com/moreinfo/surface-puck-lights/3-watt-led-puck-light-fixture/2085/

This lamp has 2 main surfaces - inside and outside. There is a small gap between the surfaces. 15% infill is needed for the base, but your slicer may also generate infill between the inside and outside surfaces. This will result in a somewhat blotchy looking lamp when the light is on, which you may or may not like. If you don't like it you have to disable infill for the part of the lamp that is above the base. A slicer like Simplify3D allows you to specify a different set or printing parameters for different areas of the printed part - so for this part you can specify no infill starting at 9.00 mm.