Hi Kennedy I know exactly what you are talking about in relation to the sensation that you are not completely asleep and you can "think." This also happens to me when I'm sleeping in in the later morning.

However, it's not actually lucid unless you realize you are dreaming. Once you have the realization, you are lucid. It's different than just being able to think differently or have control, if you understand what I'm trying to say.

It's definitely easier for me to become spontaneously lucid during these times, so I wouldn't be surprised if you experience LDs easier this way too.