I cannot refer you to any research on this topic. Actually, I’ve never heard of LDers having a problem discerning between waking life and dreams—though dreams can seem like waking life. You can quote me for your paper, though.
Most of my lucid dreams are even more bizarre than my non-lucid, “normal” dreams, so it would be quite difficult for me to confuse my waking life with my dream life. In fact, most lucid dreamers that I know intentionally make their dreams bizarre. Commonly, lucid dreams fly around, for instance. When I perform reality checks (a regular part of many LDer’s practice) I’m never in doubt about whether I can fly in real life. I would never try by leaping off a building—I don’t even do that in a dream because, after all, what if I’m not dreaming? I test whether I’m able to fly simply by jumping off the ground. In waking life, I fall immediately downward in accordance with gravity. In dreams, I might linger a little too long in the air or float down or I might zoom straight off.
Yes, dreams can feel quite real. I have convinced myself that I’m really awake/not dreaming when I was, in fact, dreaming because the sun on my skin, the hair on my arms, etc. all felt so, so real. But I’ve never been convinced that I’m actually dreaming when I’m in the physical state. I have questioned, but I’ve never had a reality check succeed. (My reality checks include: attempting to fly, pushing my right thumb through my left hand, asking myself if anything is unduly strange about my environment, etc.)
Of course I sometimes see very strange things while I’m awake. Yesterday, driving downtown, I saw groups of people on the street in their underwear. This was strange, but then I remembered that my city was having its first annual “Underwear Run.” The strangeness had an easy explanation. In a dream, the same might happen and I might rationalize it away, saying to myself, “Oh yeah, the Underwear Run is today,” while, in reality, there isn’t any such thing. But usually, dream strangeness is more marked. For instance, I once went lucid while staring at an abstract painting in my house which was animated and swirling around. As it slowly dawned on me that I was dreaming, I wondered whether I might be mistaken—maybe this was “one of those moving paintings.” But my memory won out and I saw that I was dreaming.
Lucidity in dreams, and while awake, is distinguished by a working memory, the direction of attention and the capacity to reason. So, while awake, if a person became confused and convinced that he was actually dreaming, it would probably only happen by the impairment of memory, attention or reason.