Yes, your long-term memory and perceptive senses are still active, though the frontal lobes are almost dormant.
What do the frontal lobes do?
Something to do with your personality I think.
The prefrontal cortex is related with personnality and social behaviour. If it’s no more linked with the inner parts of the brain, your actions and thoughts will no more be perceived as yours, but as external ones. For instance, you’ll hear your thoughts like they were pronounced by another people (schizophrenic hallucinations… and HH 
).
Wow - I’ve learnt something else today 
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Hm, that’s quite interessting. So - the prefrontal cortex… it bascially makes your self aware?
I can’t reply to your question about self-awareness. 
Is self-awareness the same thing than establishing a relation between things (body, acts, thoughts) and your ego… It could be, but frankly I don’t know… 
Well, if that is inactive in dreams, it could explain why we aren’t lucid so much of the time
I’ve believed for a long time that the dorsolateral prefrontal cortex is the key to lucidity. The DPC is responsible for working memory and the “reality-check” of consciousness 
So, is that the part of the brain that controlls the ‘criticul factulty’ part of the psyche?
It might have something to do with critical faculty, though I’ve never seen a journal or research focus on or make mention of that.
That is a very interesting article, the kind of thing I love reading but I don’t feel it gives enough actual facts on the area and I feel they need to describe to us exactly how and why they believe this has stopped her having dreams. I personally think they are correct, I just want to see more info on it.
I found the answer in the Skeptic dictionnary. 
But I’m always skeptic about what skeptics write… 