I anticipate it being hard as the light will be coming from the subject itself.
Read up on balancing ambient light with flash. The light coming from the lamp might not be quite what you think of when you think of ambient light, but it's the same idea.
Briefly, the idea is that flash is very bright, but has duration measured in milliseconds -- much shorter than a typical exposure. Continuous light sources like the lamp in your photo are much less bright, but are available for the entire exposure duration. So set up some flashes to light the scene, including the lamp, and control the flash exposure with a combination of flash power and aperture. Use the exposure time (i.e. shutter speed) to manage the exposure from the light bulb in the lamp. If needed, you can also use a less powerful bulb than usual, as Michael suggested, or you can use a cord with a dimmer switch to reduce the brightness.
Once you're able to control exposure from the flash and from the lamp independently, it's just a matter of deciding how you want to balance them.