In most cases, I'd be on board with the "Everyone dreams" thing. However, science
tm has actually found evidence that some people (person?) who had part of there brain blasted away from shrapnel of a grenade or some such stopped dreaming afterwards.
So yeah, unless you're missing a certain part of your brain, you likely dream.

Another note, from my days of looking up dream stuffs, you do actually dream in NREM sleep, but it's more emotion related and not very imagey, broken up and short. Also more connected to current things going on in you life at the time. It has been awhile since I read it, but that's what I got from it.
Finally, on the topic of lucid dreaming, I barely
ever have a lucid dream, and the only times it seems to happen are when I'm not trying. First time I completely failed it after sticking my finger through my hand. Felt very...strange. Strange enough that I woke up immediately. The other time was rather boring and I stopped being lucid quickly. I keep a dream journal (that I've been rather slack on lately) and though it's usually filled with detailed dreams, often there are many short pieces recorded in it that I wrote while delirious from just waking up. It's usually absolutely hilarious to read them, especially when I don't even remember writing half of them.