Lucid dream within another dream

[Twocrimsonroses]

Hi There, I have a curious question. The other night I had a very interesting dream. I was at my school and there was a school therapist treating students. This therapist noticed that I was having some emotional problems and offered to treat me. After speaking with her for a while she recommended that we go into my dream to see if we can get to the deeper issue going on. kind of like hypnosis. In the dream I went to sleep. I went into another dream where the therapist was with me guiding me. We were in a cave and there was a cliff that fell into the depths of the earth. There were bats flying all over below. The therapist said to me "now, what does this mean to you? what is going on in this dream". All of the sudden a girl showed up next to me and looked me straight in the eyes with a terrified look on her face and said "Johnathan!" and then jumped off the ledge and committed suicide. I was very frightened and confused as was the therapist next to me. the therapist said "Who was that?! Who is Johnathan?! What did they mean?!" In a very frantic and agitated way. shocked and confused I didn't know what to say and then I woke up. But I woke up back into my old dream and then that dream continued on into something else. I am wondering what this could possibly mean. Is this still a lucid dream because I was only really aware that the dream within my dream was very clearly a dream? Or is this not a lucid dream? I asked in the second dream for something to show its self to me and something did. But I don't know anyone named Johnathan and certainly not anyone that I would expect a suicidal reaction to (even in a symbolic sense). Also, I have read one other thread that mentioned that there is no such thing as dreams within dreams and that inception doesn't exist. I just want to clarify that by saying I have had a dream within a dream that inception does exists. Nor did I even think of the dream as inception until I read that post I am simply stating what happened in my dream which was that I intentionally went into another dream where I was lucid and asking for something to present itself to me. What could this dream mean?

[Hitokage]

I once went to bed in during LD and wanted to try to fall asleep with another LD, yea like in Inception. The result was that the dream just transformed into another one. It just made an illusion of dream within dream. I am not sure actually but it just felt like a normal dream change, noting special in the second dream.