Does Lucid Dreaming decrease the regenerative effect of sleep?
It's possible that they do, depending on the intensity of the dream and the amount of brain activity.

For example, if the dreamer is thinking too much or is having a dream that's way too intense, the brain activity goes up and they're not as rested.  However, lucid dreaming can be good for sleep if the dreamer creates a more relaxed dream.  This can possibly be better for the sleeper, especially if they're someone who experiences nightmares every night.

Basically, it just depends on what you're dreaming about.  The calmer and more relaxing the dream is, the better.

Source:
-www.world-of-lucid-dreaming.com