I aim to put an end to these discussions, because they are all over this site and never seem to be answered.

I understand that:
1) You do not have to intentionally induce a lucid dream for it to be lucid. Many lucid dreams are completely spontaneous.
2) You do not have to be lucid throughout the entire dream for it to be a lucid dream.
3) You do not have to have ANY control over the dream whatsoever for it to be a lucid dream.
4) You do not have to be able to think as clearly as you would in your waking life for it to be a lucid dream.

However, a little while ago I began to get into lucid dreaming again. I would follow some routine religiously that consisted of eating well, exercising, meditating occasionally and writing in a dream journal. Due to insomnia, I gave up after about a week.
A couple of weeks later, after playing video games, not exercising that often, not meditating, not dream journaling, and doing some other stuff (that shall not be mentioned) I had what I would call a false lucid dream. I can't precisely remember what happened in that dream to be honest, but in a few weeks I had another similar experience:

Two guys and I are able to shoot webs out of our wrists in a similar fashion to spider man. We are swinging around the city when we receive a call. The person on the other end of whatever we were talking on tells us to rendezvous with the city's mayor on an island that is roughly 20 meters out from the coast.
The island is covers in sharp, jagged rocks and the sky is dark. a thunderstorm rages around us. The mayor begins to talk but I quickly become bored with the conversation (the webs we shoot are littering the city and he is reprimanding us), so I attempt to launch myself into the air using my web.
Suddenly, it occurs to me "I could just fly."
So I do a couple of diving forward rolls (a technique I had practiced a couple of weeks before in that first "false lucid dream" (Now I remember)) and I launched myself into the air.
I could fly and it was so easy. Unfortunately, I became overly excited and lost the dream.

Now, the issue here is that whenever I have had a lucid dream before, I have thought "I AM DREAMING" and the realization has brought the whole scene into crisp, clear focus that leaves me with an amazing sense of excitement and amazement.

In these two "false lucid dreams" the thought never occurred to me. The environment never became more vivid. The thought that I could have been dreaming never crossed my mind. There was just a seamless transition from dreaming to being "conscious", but it wasn't a consciousness that was similar to lucid-dream-consciousness. In the first one I thought "if I imagine an army over the rise behind me, it will be there", but the thought "I am dreaming" never appeared.

It seems, as I see it, that I must actually think or say the words "I AM DREAMING" in order to become conscious within the dream, otherwise, it's not the same. Perhaps other people are having the same problems and the answers to this thread will help them.

So please, I have spent a lot of time planning this out and writing it, give me an appropriate and equally thorough answer.