Counting Sheep: The Science and pleasures of Sleep and Dreams. Paul Martin.

Do dreams occour only in rem sleep, or might we dream all night long? The Idea that dreaming is exclusively linked to REM Sleep has been overturned.
A lot depends however on what is meant by "dream". We tend to associate the word with bizzare and visually rich narrative dreams of REM sleep, in contrast to the more mundane thought processes of waking consciousness. When people are woken from NREM sleep and asked if they are dreaming , they reply yes only on about 7-8% for occasions. However, if instead they are asked wether they were thinking about anything, they say yes far more often. In fact people woken from NREM sleep report some form of mental activity on 40-60% of occasions.

The "dreams" that occour during NREM sleep are different. They are generally less vivid, less surreal, less unpleasant and less "dream-like" than classic dreams. They lack bizarre story lines, the strong emotions the strong emotions and intense imagery. In fact they are more like conventional waking thoughts or fragments of ideas. NREM dreams are also shorter and less complex than REM dreams".
There's three pages of scientific references to the chapter this text quotes.
Enough to satisfy THOR even.



It seems the answer to the OPs question is this:

It may be possible to have a Lucid dream outside of what we technically call REM sleep, in the brief transition periods between NREM and REM.

But generally NREM dreams are very different from REM dreams.

It may not be possible to have a "Lucid dream" as we understand it during NREM.
But it may be possible to be aware that your in NREM - in a meditative way - which might be described as a type of lucidity.