I don't know what it means to have a "false lucid dream", but for me I have a category of dreams I call Power Dreams. These are dreams where I have some of the powers of a lucid dreamer, which often is in the form of not being afraid because of some innate knowing I can't be hurt, and then acting from that and overcoming situations. There seems to be some level of awareness I'm dreaming but it doesn't rise to the level of conscious thought. I believe there are definitely levels of lucidity and the lowest I refer to as Power Dreams.

Your description reminds me of that.