I had a very interesting revelatory dream a couple of weeks back that led me to this question among others and insights I thought I should share.

So the dream starts with me not lucid when suddenly a friend of mine appears and tells me that there is an area of high lucidity. So he takes me to a place where I see a corridor of white light and from there I see a child and an adult coming from it. I then become lucid and felt the atmosphere of the dream in a way I had never noticed as clear before. I noticed the clear different in lucidity levels and how that affected the dream. So in the place I was the scene was all crackly and unclear and as I move towards the corridor of high lucidity I can feel that the area is more dense and I feel heavier, but more stable and solid. Everything was clear here just as in waking life (I've had high lucidity dreams like this before but never felt the clear difference and could put it into words before). So as I moved further into the corridor I came upon a transitory room where there was a DC voice guiding me and some people into this area of high lucidity. So after putting on a full body suit and going through a revolving door (typical dream stuff) the scene changed and me and the people from before seemed to be initiates of this DC who we could now see. He begun to teach us and talk to us about lucidity levels. He asks us whether we are ready to go to the next level (meanwhile the scene is just as vivid as waking life. No changes in the environment if I turn my head or something), and tells us that with high lucidity there will be both good and bad experiences and things that come with it, just like anything else. I decided that any knowledge or experience is worthwhile so I was determined to go through with it. He then asks us a question about what is the most important factor that influnces things in a dream and I am quick to answer "the person's innermost desire" which be the right answer. He then goes on to tell us that in order to be strong with lucidity we need to be physically strong too. I then realise that I should push myself a bit more physically in waking life (I am actually very active, but could do more). So he gets us to start running laps in the dream and most of the other people seemed to immediately give up or be unable to do it. After 3 laps in the parking lot I was growing tired and heavy but am determined to carry on by sheer will. I soon wake up after find this DC's name which he didn't want to tell me and then finally said "Sorcerer".

This was a very fascinating lucid dream for various reasons, which brought on many questions and insights for even a relatively experienced lucid dreamer like myself (at least I consider myself to be one)

tl;dr: Does physical activity in waking life actually affect lucidity levels and our awareness in the dream other than affecting sleep quality?
Or is it just sheer WILL brought on from physical exercise that helps with lucidity? (focus, dream control, etc.)
Is there "physical" spaces in the dream which are more or less stable then others - ie high and low lucidity areas as seen in my dream?
Then there's the typical questions of whether there actual worlds in the dream realm and actual characters in their own right. (I have already made my own conclusions about this)