When your trying to define a Lucid Dream, use this basic guideline to help:

When your dreaming, are you able to have the though of "This is a dream.". If so, then its a Lucid Dream. Lucidity mearly implies consciousness. If you are in control of your own thoughts are capable of coming to the realization that your dreaming, then its a Lucid Dream, regardless of the amount of control you have at the time.

Now, about your WILD attempt:

Chances are, you were at the early stages of Sleep Paralysis/REM Rebound, in which you were getting closer to the transition state of being put into a dream, which is why your eyes seemed to be darting around, because thats why they do during REM sleep, aptly named "Rapid Eye Movement". As far as a false awakening, its really difficult to say without more information about your previous dreams. Chances are, you did what I do alot: You get into the WILD state, and even though your close, you can't quite push past, and "wake up" the rest of the way, and then go to sleep.