The definition of lucid dreams refers to consciousness during dreams.. being conscious that you're dreaming. It's interesting though to think about it the other way too.
Dreaming that you're conscious... an interesting example of dreaming that you are conscious would be believing that you are awake (as in a normal non-lucid dream), doing a reallity check but still be convinced that you are awake. ... in fact I think.... dreaming that you are conscious would be exactly having a non-lucid dream