Is it still considered Lucid Dreaming if you've woken up and fallen back asleep, but while you were still awake, you kinda told yourself you're lucid.

Ok, since I'm not gonna be technical here....well, live with it.

You know when you wake up in the morning, really early, and you're all like "Crap, I woke up, I'll never get back to sleep" but you fall asleep. Except that while you're asleep, you can still kinda hear what's going on around you and stuff.

Well, that happened, and I THINK I gained lucidity, but I'm not sure...

Will someone please help?