Becky Stern was kind enough to give me the following parts list for the project:
1. Universal Qi Wireless Charging Transmitter ($27) This part plugs into a USB power source and emits 3.7V power through a copper coil. This part goes inside the charging base.
2. Universal Qi Wireless Receiver Module ($15) This part receives transmitted power through a copper coil. It goes inside the lamp.
3. Micro Lipo w/MicroUSB Jack - USB LiIon/LiPoly charger ($7) This part stabilizes the power coming through the wireless receiver, ensuring that it stays at a steady 3.7V.
4. Lithium Ion Battery - 3.7v 2000mAh ($12) This is a standard rechargeable battery pack that gets is power through the Micro Lipo charger.
5. 1 Watt Cool White LED - Heatsink Mounted ($4) This is a heatsink mounted LED that is pretty bright with 3.7V. It plugs into the battery.
6. DC3-250V SPST Panel Mount Self-Locking Metal Push Button Switch 16mm ($9) This is a standard latching switch that turns the LED on and off.
Any desktop FDM printer will do. The lamp is a 5" X 5" (127mm X 127mm) cube, so any printer with a bed at least that size should work just fine.
All you need for this project is a soldering iron and a small screwdriver.