This is both draconian and absolutely retarded. Reeks of a venture capitalist who doesn’t know anything about basic biology, psychology, or technology. The lucid dreaming state is not one of intense cognitive performance and reasoning, and even if you were able to do that heavy of a workload while “asleep”, your brain wouldn’t actually be getting any sleep. When you “wake up” you would be absolutely mentally exhausted and have to go back to actual sleep.
I quit my company a week ago because as a company of 13 people the communication at all levels was so poor compared to my previous job working with over 20 and several departments. I’m not usually one to judge people’s degrees, but our boss has a biosciences and GIS degree and somehow wandered their way into software management and has the biggest superiority complex I’ve ever seen. These people plague the software development landscape so, my condolences for your CEO who is probably too busy looking at golf clubs and scheduling tee times while writing up an email about how hard executive management works to get back to you.