Shooting lamps sounds like a product shot. And product shots generally mean very close control over the exposure. How much time and/or effort do you want to put into the shots?
The basic problem sounds like a dynamic range issue. My first question would be, do you prefer to do multi-shot HDR's or single-shot?
Starting with single-shot options... because the bulb and/or shade is always at the top, this could be a situation for a graduated or split field neutral density filter. That's a filter that darkens half (or a portion) of the frame, and in this case the top half. You can get a cheap square filter system for $20 (Neewer), or $50 (Cokin) or hundreds (Lee, etc.). I'm assuming that you'd need to use a 2- or 3-stop filter.
The advantage to this approach is that you'd be getting the shot in-camera and possibly getting several shots done quickly if it's going to be many lamps. You'd probably still want/need to do some post-processing to fine-tune lifting the shadows or taming the highlights. But the time at the computer would/should be pretty minimal.
The second single-shot option is to throw flash at the non-illuminated portions of the lamps. You'd need to "flag" the flash (or set up blinders) to control where the flash goes. You'd have to spend some time setting up the shot and probably making flag adjustments for each shot. But you'd be able to keep post-processing time to a minimum.
Going with multi-shot, this is a classic fit for HDR photography. Using a program like Photomatix or what is now built into the Adobe products, you can take multiple pictures of each lamp for the highlights and details and combine the separate frames in post-processing. If you have Lightroom or Photoshop (as part of the Adobe bundle) or Photomatix, then there's nothing else to buy. The individual frames can be captured quickly (with bracketing), and you'd need to spend more time at the computer.
These are just some starter ideas that could be adapted to how many final images you're after or other details.