I tend to consider myself a "natural" lucid dreamer, though it may be different from what you'd get with this method. Haven't read everything but wanted to post my experiences.
As long as I remember, I've always known when I was dreaming the vast majority of the time (with a few notable alarming exceptions). There's no spot-checking or anything, it's just, you know... everything inherently feels different and like I'm dreaming, so I obviously am.
I had the thing a couple other people mentioned where I had nonstop horrible nightmares as a kid, so I learned to wake myself up from inside dreams out of self-defense. I can still clearly remember the dream where I first pulled it off. My usual method was making fists really hard and squeezing my eyes shut, and occasionally biting my hands if that didn't work.
My breakthrough for actually exerting control over my dreams came years later. I was in one of my "riding in an out of control car on a twisty road with cliffs on either side" dreams, and the car was coming up to a sharp bend in the road. I was afraid I was going to go off the edge, but then for whatever reason decided I probably wouldn't even if it would make sense to. And then I didn't. Which was an incredibly minor thing, except it was instantly apparent to my dreaming self that the only reason I hadn't gone off that cliff was that I didn't expect to, and therefore
my expectations were actively shaping my dreams while I experienced them. So then I started paying attention and seeing that effect
everywhere across multiple dreams. Bad things happening when I expect them to, or things not happening when I don't.
Next step then was intentionally modifying my expectations, which was harder than it sounded. There's a sort of clap-your-hands-if-you-believe aspect to it. You have the power to shape the world around you to your whims as long as you're
really convinced it will happen, but if you doubt this ability then it won't work (because it's based on expectations, not intentions). I kind of had to culture an a-god-am-I attitude to get it working with any kind of consistency. I've used it for various things from teleporting out of danger to transforming into various flying monsters and blowing off whatever's otherwise happening.
That said, my dreams do tend towards cool fantasy/sci-fi settings and plotlines, so a lot of the time I don't actually
want to interfere, except maybe to nudge things along and make them more interesting. Even nightmares - I'm a horror fan, so why would I intentionally destroy a fully immersive genuine-feeling horror experience? (answer: it got 2spooky)
I guess my dreams are more quasi-lucid... I know I'm dreaming and can choose to change them however I want, but usually don't and they play out like normal dreams. I have had the more conventional fully-lucid dreams too, though, where the entire world is incredibly sharp and intense and you feel like anything is possible but at the same time you're barely holding it together and everything could shatter at the slightest touch of a thought.
Also, my method for manipulating dreams (believe and it will be true) has at least one major drawback. One of the things I want more than anything else is to experience what it feels like to inhabit a completely non-humanoid body. I suspect because I want this so badly, I'm subconsciously blocking myself from achieving it (because of a "too-good-to-be-true" sort of self-doubt). So whenever I transform into something else, I just feel like I'm in a human body occupying the same space as the creature's body, with the mismatch kinda being handwaved away. When stuff has more than 4 limbs, I can only control four at a time and have to shift my arms from "inhabiting" the forelimbs to the wings and back intentionally, for example. It's led to some interesting things (as a quadrupedal werewolf I was physically walking on my fingers and toes) but on the whole is rather disappointing, and I'm not sure I can overcome it.
I also had what I believe was a form of sleep paralysis once, but it didn't scare me and it made me laugh afterwards. (I hallucinated the sensation of a tapeworm crawling out of my mouth and heading under my blankets, and my sleepy brain's reaction was to go "oh nooo i need to catch it but i can't move, it's gonna get awayy" and then realize its texture was inconsistant with a real tapeworm and go "oh, oh well" and fall back asleep).