Way back in High School I wrote a paper on Lucid Dreams.
Fascinating stuff. But I do believe that they occur
during REM dream state. (Which would mean during sleep.)
The lucid dreamer can recognize during the dream that
they are in fact *in a dream state*. At which point
they begin to express control over thier dream environs.
Lucid dreamers often can *learn* to recognize their dream
state and have considerable success in *returning*.
This fact is quite true.
Teep