...but couldn't remember it, when you woke up? What this would mean is, you're a successful lucid dreamer, only you don't yet know about it?

Does it happen this way, or are lucid dreams generally easy to remember upon waking up? Otherwise, we may not even know we're lucid dreamers despite being so!

Any idea on this? Do I rest assured that if I have a lucid dream, it will certainly be remembered upon waking up? If not the dream content, will we at least remember that we had a lucid dream?