I think it all comes down to about the same thing. When you become lucid by recognizing a dream sign or something odd in a dream, I think it's because you happen to be able to access enough of your true memories from waking life to remember that what you're experiencing isn't possible as a waking-life event and that you must therefore be dreaming. Normally, when one isn't lucid, the mind provides an appropriate set of false memories in a dream that ensures the dreamer always thinks they're living their actual waking life and never remembers what's actually happening… until they wake up.

In your case, it sounds like you're often able to remember directly that you've just gone to sleep and must therefore be dreaming, without needing to have something like a dream sign or oddity clue you in first. I've had this happen to me occasionally, mainly during very light sleep toward the end of my sleep period. In deeper sleep, it usually seems to take me a bit of abstraction first (like noticing something odd, because I just so happened to remember that it is in fact odd) before I can ultimately reach the conclusion that I must be dreaming. Remembering that you're dreaming more directly is a good sign, I think, because if you can remember the truth of what's going on that easily, you're probably in a position to have a very strong level of lucidity that gives you a high level of dream control and allows you to get the most out of LDs.

In any case, though, it seems that attaining full lucidity in a dream starts with remembering in some form. So, my guess would be that to take advantage of this would mean continuing to practice and maintain this ability to access your waking-life memory during a LD. Maybe someone more experienced here will come along with a better answer, though.