I started by designing a 3D model of the lamp using Autodesk 123D, which is freely available online.
To make a cross section of the lampshade, I used the Draw tool and the 3-Point Arc tool. Notice the grooves on the inside of the lamp; they're carefully sized to hold the electrical lamp components in place once the lamp is assembled. Everything else was just roughly estimated and tweaked as needed.
To turn the cross section into a 3D object, I used the Revolve tool. This tool spins a profile around an axis of your choice, producing an object with rotational symmetry.
I made the stand using a combination of hand-drawn splines and hemispheres, adjusting it until it looked sufficiently lampy. At the time of writing, Autodesk has not yet included a tool for accurately measuring the lampiness of a 3D model, so I had to judge that entirely by eye.
I joined the two parts together using the Combine tool (set to Join mode), then exported the object as an STL file. I've included the STL file here, with 1 STL unit equal to 1 human inch.