I think I had two lucid dreams,and im pretty sure how I got them.

First off, I woke up too early and went back to sleep. So my first lucid dream involved me jumping off of a cliff. I remember trying to tell myself not to wake up while I was falling, and while I was falling I was enjoying it and it was so much fun. When I hit the ground I did not wake up, like I usually do.

Would this be a lucid dream because I must have known that falling off a cliff wouldn't kill me, but I enjoyed it instead?

For my second lucid dream, I remember waking up too early once again, and then while I was falling back asleep, I remember trying to concentrate hard on creating another lucid dream where I would fall. Then my dream started with me riding an elevator to the top of a very tall building, and then I pressed the "down" button and did a free-fall and hit the ground, but did not wake up.

Both of these seem to me like lucid dreams because I enjoyed the fall in the first dream and created the second dream so I would fall. And both times I woke up, was tired, and went back to sleep. Is this the best way to get lucid dreams for most people? Also, for my second dream I felt like I had to concentrate hard to get the dream to take shape. I literally "thought" my dream while semi-awake and it happened. Is this lucid dreaming as well?

If someone could answer both questions I would really appreciate it.