The thing is that when you say you might know a better way of defining the term "lucid dream", that's just like saying you know a better way of defining the term "odd number" (why not keep up the comparison now right?). >.>
"Lucid dreaming" simply has a meaning, and that is (for as far as I've seen so far): To be dreaming while knowing that you're dreaming.
Now obviously those who (try to) master lucid dreaming (that's us...) don't do it to know that they're dreaming, but for the benefits often connected to that fact (e.g dream control), and that is why it's not really that important to know whether or not your dream was lucid or not. (Lucid) dreaming is about the experience you get, not about getting to categorize something (in my opinion anyway, but I feel most of you would agree).
But once again, for those who really feel the need to know whether or not they were "officially" lucid, the answer depends entirely on whether or not they realized they were in a dream at some point.