If you're interested, Dr. LaBerge talks about much more of the experiments he did for his PhD dissertation in his book Exploring the World of Lucid Dreaming.
I'm not aware of whether any one's looked at the pre-rontal cortex like you mentioned, but LaBerge's experiments with the polygraph where subjects perform previously agreed upon actions while lucid would seem to suggest that in a (medium to highly) lucid dream, your critical faculties are indeed working.
I haven't read his book, I am familiar with some experiments done during lucid dreaming though. Not that it really matters, nor does the fact that critical faculties are working (which you don't need to make any measurements to conclude, behavioural clues would do), it's what you measure that makes a difference and I don't see what relevance a polygraph would have when it comes to neuroscience. In the case of the recording of eyemovements of lucid dreamers with an electrooculogram connected to a polygraph (which is what he did in the experiment you mention), which might as well be a computer, so it would be better to refer to it as polygraphic records, but anyway... this still has no relevance from the perspective of neuroscience.
Laberge has done some other good work though, some of which relates to the field of consciousness studies and world simulation theories of consciousness/representationalist theories of perception. So yes, his research is interesting, but no, he has not done the prefrontal test, nor has anyone else, that's why I mentioned it. Any lucid dreamer care to get strapped in ?
That's only wishful thinking though, I don't even have access to EEG at my university, even less some more expensive form of functional scanning device.