They vary in length. You might have gotten unlucky and happened to have that dream and become lucid right at the end of that REM period when you were just about to wake up. That happens all the time to me, especially since the times I'm most likely to be lucid seem to be right when I'm close to waking up. But over time, I do have some LDs that are longer than others, so the more LDs I have, the more long ones I have.

I personally don't worry too much about stabilization if the dream feels stable already. If I start feeling like I'm about to wake up, I'll often stop for a moment to take in the dream scene and refocus. With time and familiarity, it seems to become an almost automatic action.