I have had some odd situations myself that are very hard to catogorize.
When you say ,"you wake up" when you realize you are dreaming , is this on purpose or it just happens when you realize you are lucid?
This sounds like a false awakening. When you find yourself in another dream. But do to lack of control this may be considered a deep lucid. Don't quote me on this. I have had similar expirences and this was what I was told:
In a deep lucid you are beyond the point of normal sleep. Deeper. But you manage to still become lucid. However because you are in such a deep sleep you tend to loose some of the Lucid control you might otherwise have.
To go deeper is considered a near death experiance. This I am still trying to understand. There are a few posts about it if you use the search method. But none of the posts explain them to the depth that I would consider helpful. But it may help you.

This may also be a completly wrong analysis too.