Yes—this is a useful product-lighting problem, and you can often solve it without compositing. Treat the lamp as the ambient/continuous light source and use external lighting (flash or other off-camera lights) to illuminate the product and surroundings.

A practical approach:

• Light the lamp and scene with external lights.
• Control the flash/external-light exposure with power and aperture.
• Control how bright the bulb appears with shutter speed, since the lamp’s light is continuous.

This is the same basic idea as balancing ambient light with flash.

Another helpful trick is to use a lower-wattage bulb than normal. It will usually photograph more naturally and be less likely to blow out. If the lamp is shown in a room or styled scene, light the rest of the scene separately so it looks like the lamp is providing illumination without relying on the bulb alone.

If a single exposure still can’t hold both the bulb detail and the product detail, shooting two frames—one optimized for the lamp itself and one for the product—and blending them is a reasonable solution.