In “The Art of Dreaming” Carlos Castaneda mentions a technique that is supposed to “solidify” a dream, making it as real and stable as possible. You are supposed to fall asleep while in a dream, with your dream body in the same position as your real body - on your right side, on your left, on your back, whatever.
I am curious if anyone has tried something like that, is it actually possible to fall asleep in a lucid dream?
I haven’t tried it yet, but it’s definitely possible to fall asleep in a LD. You might even end up getting a LD inside a LD 
In fact, dreaming comes much faster if you fall asleep inside a LD, but the problem is often to maintain lucidity. Another thing is that you might get tricked thinking you became lucid after you went to bed irl, while in fact you went to bed during the previous dream. These kind of LDs are usually called FLDs (False LDs).
Why should it be not possible? Everything is possible in a dream. Though I’m not sure if it is possible to transform your body this way , many people tried it, and often they really got a stable and realistic dream.
The problem is that “falling asleep” is also a good way to wake up or have a FA, so you must really know what you are expecting to get, when trying it.
Maybe, I’m just a little bit scared of this technique (it’s also called “twin position”, by the way) after Castaneda’s books, but every time I’m going to try it, I cannot find any bed 
And Jeff wrote he can reach NDE-like state by having WILD inside WILD inside WILD…
I read about someone who would go to sleeep in a lucid dream in order wake up.
As they fell asleep, they would drift off to wakefullness.
Flo tried Castaneda’s “twin position” without notable result.