The challenge here is to wire up a WMF Ikora glass lamp base that holds 2 bulbs: one in the base of the lamp, and the other conventionally above the base. These can be switched so that the lamp can have both bulbs lit, or just the upper, or just the lower, or both off. There are a few ways that this can be achieved. I've assumed that as the lamp is glass it will be double insulated, but the relevant components can be earthed if required.
Using a single pole, 4 throw rotary switch, we can wire up the lamp so each switch position corresponds to one state of the lamp. Note that the switch must be able to run at the lamp's AC voltage, and the maximum power of both bulbs combined - many switches are designed for much lower voltage use.
The switch will either need to be mounted on the body of the lamp (which requires a hole of the right size), or in an enclosure that has the cable passing through it. Knobs are generally sold separately to the switch, so you can make one up or buy one to suit the style of the lamp.
Here we use a component that has two toggle switches side by side in an enclosure that fits onto the power cable. Each switch controls one bulb, enabling the desired lighting options to be achieved.
This probably doesn't fit well with the Art Deco look of the lamp, but I'll mention it to show what can be done with a bit more technical skill. We can use a microprocessor such as one of the Arduino range to give us the processing power - Arduino gives a very simple development environment, great for quickly developing projects that are one-offs or limited volumes, or prototyping for larger volumes. This would need a power supply to provide the 3.3V DC it runs off. Then as input we could have a touch switch or proximity switch that would give us an input every time it was touched. In our code, we'd just wait for the input, and then switch to the next combination in our sequence. This would be done using the digital outputs of he microprocessor to control relays to switch the bulbs on and off.
Assuming the solution is the 4 way rotary switch, here's one way to do the hardware.