^^ I call them False Lucid Dreams, though I'm assuming I didn't make up the term.
In a nutshell, a FLD is a non-lucid dream
about being lucid, but with a total absence of self-awareness. This is likely a fairly controversial term here at DV, so I don't expect you to buy into the idea. I have a feeling, though, that they occur a lot more often than people think (I've been LD'ing for well over 30 years (gasp) and I still get them often. Here's how they happen:
We all want to LD very much, and spend a lot of time thinking about them, talking about them, and hoping for them. Mix that with waking-life activities like RC's, setting intent, conscious expectation, and induction techniques, and you wind up with an unconscious mind filled with day residue about LD'ing, expectation, plus some possible neural hard-wiring for LD'ing.
Now let's say you've got all that in your head, but you manage to go sleep without bringing any self-awareness along for the ride. Well, the fact that you're lacking awareness might not stop your dreaming mind from fulfilling all your wishes and providing you with a dream that fits all the proper parameters for an LD -- except that it's just a dream. That's right, you're having a dream about LD'ing.
With practice, it's not that hard to recognize that you're having one. There are some basic memory tests you can use to confirm that what happened was just a dream, like if the memory is behaving more like a non-lucid than a LD (ie, it's fading fast), or perhaps you remember a severe lack of control or way too many surprises. For more details, you might check out my thread, "
A Treatise on Proof" for more details (and some interesting posts from those who think I'm wrong about this).
Bottom line: when you have a FLD, you are dreaming you are lucid, but really are not. I suppose they can be convincing enough that it doesn't matter when it happens, but I'm pretty sure they happen frequently.