Yes, eye movements are related in normal dreams also. eg, in EWLD LaBerge recounts a story where they tracked someone’s eyes moving left-right about 20 times and when they woke up they reported watching a tennis game (non lucid) 
However, using this movement to re-draw the dreamscape would be useless, I think. For example, what do you look at if a friend comes up to you? You look at their face and specifically their eyes. So, if you redrew it you would get two points (eyes) and perhaps some other features on their face. You don’t look at the contours of objects, but at focal points, things that are important. And even then, those movements are similar. If you turn around and someone is going to stab you, if you watch the hand your eyes will move in the same pattern as if you turned around to watch a wave crash on you. I don’t think we are on the right track here…
Thanks! that was what I was looking for!
(I do even own that book… shame on me! 
)
Just one case does not prove anything, but I think it’s a big clue!
That is a good question!
I think our eyes are not subject to SP during REM. So they move as a reaction to what you see. No input from the eyes since all images are generated in our visual cortex, but still some output to the eyes as a reaction on those images. (Hey - there’s something on my right… eyes move to the right)
This also fits in the tennis game from EWLD kmcdonald quoted.
But I’m only guessing here.
After some searching I found the following article. Dr. Roffwarg showed that eye movements in REM sleep correlated precisely with the visual imagery of dreams.
Roffwarg, H., Dement, W., Muzio, J. & Fisher, C. Dream imagery: Relationship to rapid eye
movements in sleep. Archives of General Psychiatry, 1962, 235-257.
Wow that is a really old study (1962), if anyone has a link to a copy of it online, could they copy and post it, please? And the reason our eyes aren’t in SP during dreams is because they are part of our brain (yes, really, you can walk up to someone who has their eyes open and truthfully scream “Oh my God I can see your brain!”).
I did some extensive internet search, but I could only find references to that study. 
Maybe I can find a paper copy in the university’s library…
LOL lol: 
;-D