Please no Inception comments on this! Just because you're dreaming that you're dreaming doesn't imply anything Inception-based is going on. The movie got a lot of oneirology wrong, largely due to the fact that it is fiction.
It happens. Dreaming that you're
dreaming while in a dream isn't impossible. While it might be relatively
rare, it's not even improbable.
Now, when most people
(from what I have read, studied, and discussed with others) lucid
dream, they break the story of the dream and go off and do their own
thing. When this is done, there's no need to "go to sleep" within the
dream, because you're already present in a giant sandbox of a reality.
on the other hand, choose not to break the story of the dream. I
maintain lucidity, but let the story continue, because I use the random
connections found and made in dreams to inspire art--my conscious
imagination sometimes simply isn't enough. So, if the dreamstory decides
I'm sleeping within the dream, it's possible I may dream too, though at
that level, it works a little differently.
dream is never lucid for me, but my recall of it when I return to the
outer dream is almost always nearly perfect. Recall of the inner dream
when I wake and leave the outer dream is very often more vivid than the
outer dream was.
And to answer your unasked question,
even though I told you not to think about it, I've never had a third
dream inside the second one. In order for that to occur, I suspect the
second dream must also be lucid.