I got so good with lucid dreaming when I was younger that I could pretty cleanly drop straight through full consciousness into the half sleep stage of paralysis and then into unconsciousness in which I would immediately find myself lucid in a dream, but having been aware of everything in between.

This is quite difficult to do from what I recall because you have to completely clear your conscious mind of all thought while maintaining awareness of what you are intending to accomplish in some lower part of your brain. It's quite hard because you have to be aware but not thinking. Practicing meditation is about this exact kind of thing, and while I have never really done meditation, I expect practicing it would help a lot for this.

I could actually feel the point at which I went into the paralysis and had no input to my body anymore, and the oddities of perception beginning to shift due to my half awake brain.

When I actually dropped through that floor into sleep (which for me did not take that long after the paralysis from what I could sense), the feeling of moving through into actual sleep was pretty wild to experience as it is something usually not remembered or noticed, and I have no great way of describing how it was for me other than it kind of felt like I folded or collapsed inward on myself.

Sort of like if everything around you and every sense you had rushed away suddenly. My sense of sight, touch, smell, taste, hearing, balance - but not like it all just disappeared instantly, more like it was all "pushed" off of me over the course of a moment or two, which is why it's just such a difficult and strange thing to try to describe. In a way it did feel kind of like falling - in the least a sense of motion is the closest thing that could be used to describe it, but that also is not really it either.

Then I was immediately aware of the dream and knew that I had accomplished the goal, after which I was free to release the strong awareness I had been maintaining and turn my focus to what I was actually looking to do in the dream otherwise.

So yes, you can learn it and get quite good at it, but I think it depends on the person, a lot of practice, and a lot of trial and error. There are other methods that can be used to discover the dream mid-way through as well described in this thread, but you can enter the dream at the beginning in my experience too.