In my experience, it is less important to be aware that we are dreaming than to be capable of exercising choice, pursuing goals and considering consequences, whatever state of reality and consciousness we may be in.
I used to avoid the term “lucid dreaming” because it was often associated with approaches that promised to teach people to “control” and “manipulate” their dreams. The discussion has matured greatly since then, though if you cruise the web you’ll find plenty of hucksters promising to teach you how to be a master of the universe or have guilt-free sex with anyone through lucid dreaming.
I chose the title Conscious Dreaming for my first book on all of this. In my mind, being conscious means more than being lucid. It means being aware that at every turning, in every state of reality and consciousness, you can exercise choice. At the very least, you can choose your attitude, and that can change everything. You want to be prepared, always, to test the limits of possibility.
The ability to embark on dream journeys at will, travel to certain locations, contact transpersonal beings and exercise wakeful powers of goal-setting and decision-making in the dream state is what is prized by traditional dreaming peoples. In other words, they rank volitional dreaming above lucid dreaming, to employ a helpful distinction suggested by anthropologists Roger Ivar Lohmann and Shayne Dahl.
As a lucid dreamer, you may experiment with creating environments in nonordinary reality where you can live out your wildest fantasies or engage in training or meditation. I am greatly in favor of practicing reality creation on the imaginal plane. However, you don’t want to fall into the delusion that everything you experience in dreaming is merely a figment of your own imagination, or that everyone you encounter is a projection or aspect of yourself.
You will come to understand that dreaming – lucid or otherwise – is a portal to other realms of reality in the multidimensional universe. They may have their own physics, whether similar or wildly different from the physics of everyday experience on Earth. These realms include the territories where the dead are alive.
This is common knowledge in ancestral and indigenous traditions, which understand that the dream world is a real world and may actually be more real than much of ordinary life, where we are sometimes in the condition of sleepwalkers. In dreaming cultures, it is recognized that the most important events in our lives may take place in dreams.
Anthropologist Irving Hallowell wrote of the Ojibwa, “When we think autobiographically we only include events that happened to us when awake; the Ojubwa include remembered events that hat have occurred in dreams. And, far from being of subordinate importance, such experiences are for them often of more vital importance than the events of daily waking life. Why is this so? Because it is in dreams that the individual comes into direct communication with the atiso’kanak, the powerful ‘persons’ of the other-than-human class.”
Shamans say that in dreams that matter (waking or sleeping) one of two things is happening. Either you are journeying beyond your body, released from the limits of space-time and the physical senses; or you receive a visitation from a being — god, spirit, or fellow dreamer — who does not suffer from these limitations. In the language of the Makiritare, a dreaming people of Venezuela, the word for dream, adekato, means literally a “flight of the soul.” An elder of the Kwakiutl told Franz Boas that "dreams are the news the soul brings us when it comes back from its journeys.". 
Among the Semang-Negrito peoples of the Malay peninsula, "walking into a dream" means entering an altered state of consciousness and a separate reality. What is experienced in dreams is at least as real as what goes on in the day. One of the souls of the dreamer travels in other worlds. 
If you have been primed to think that what goes on in dreams is all about your own thoughts and projections, you may be shocked into awareness that the dream world is a real world when you find yourself in a lucid dream in which other players are clearly beyond your control.
For Jung, the dawning came in his encounters with the mentor he called Philemon, who appeared to him as an old man with kingfisher blue wings and convinced the psychologist, as Jung put it, of the objective reality of figures who appear in inner experiences. "it was he who taught me psychic objectivity, the reality of the psyche." 
I once dreamed that I was rattling along at high speed in a yellow New York City cab. I became lucid when I noticed that the taxi driver was a dead man yoked to the steering wheel by a rope around his neck. I yelled for the cab to stop. When it did, I heard the kind of recorded voice you get in New York cabs. It said, "This is not a dream. You are in the afterlife."
I proceeded to have adventures in a number of strange Underworld locales and bardo states. Getting out of here was not straightforward. I had to ask for help. It came in the elegant shape of a being I had met many times before, who is recognized in certain traditions as a form of the sacred Gatekeeper. I was lucid throughout this odyssey, and volitional in the sense that I remained fully conscious of my power to choose my course. But the other players and the environment itself had their own reality and solidity.
A bigger experience in a state of dream lucidity brought me to my first encounter with the spiritual teacher I have called Island Woman in my books. This episode began in the hypnopompic zone, when I stirred from sleep in the middle of the night. Among the stream of images rising on my inner screen, I chose a double spiral of the kind I had seen on a guardian stone at the entrance to Newgrange, the megalithic temple-tomb in Ireland.
Instantly, I found myself floating above my body - a reminder that in dreaming (lucid or not) we often travel beyond the body and brain. I enjoyed the very sensory experience of flight. I lifted over trees and rooftops, soaring and swooping like a bird. I felt some pain when my wing feathers rubbed the dried needles of an old spruce tree.
Then I felt the tug of someone else's intention. I chose to follow the call. It brought me on a long flight over pristine woodlands - modern highways and developments were gone - to a cabin somewhere near Montreal where a wise and ancient woman spoke to me over a wampum belt. I did not understand her language until a series of later experiences - and some helpful synchronicity - led me to my first friends among the Six Nations of the Haudenosaunee, or Iroquois. They had me repeat words I had recorded phonetically. Eventually we determined that my interlocutor was speaking to me in an archaic form of the Mohawk language, "the way we may have spoken it three hundred years ago."
I was required to study Mohawk to understand the teachings
of an arendiwanen, or "woman of power", who had called me
in a lucid dream into a real world beyond linear space and time. This
transformed my life. 
1. Roger Ivar Lohmann and Shayne A.P. Dahl, "Cultural Contingency and the Varieties of Lucid Dreaming" in Ryan Hurd and Kelly Bulkeley (eds) Lucid Dreaming: New Perspectives on Consciousness in Sleep (Santa Barbara: Praeger, 2014) vol 2., 24-25.
2. A. Irving Hallowell, "Ojibwa Ontology, Behavior and World View" in Stanley Diamond (ed) Culture and History: Essays in Honor of Paul Radin (New York: Columbia University Press, 1960), 207-44.
3. Marc de Civrieux, "Medatia: A Makiritare Shaman's Tale" in David M. Guss (ed) The Language of the Birds (San Francisco: North Point Press, 1985) 74.
4. Franz Boas,"Ethnology of the Kwakiutl" in F. W. Hodge (ed.) Thirty-fifth annual report of the Bureau of American Ethnology to the Secretary of the Smithsonian Institution (Government Printing Office, 1921) pp. 724-725.
5. Diana Riboli, "Dreamed Violence and Shamanic Transformation in Indigenous Nepal and Malaysia" in Lucid Dreaming: New Perspectives, vol, 2, 75.
6. C.G.Jung, Memories, Dreams, Reflections trans. Richard and Clara Winston (New York: Vintage, 1973) 183.
7. For the full story, see Robert Moss, Dreamways of the Iroquois (Rochester VT: Destiny Books, 2004) and The Boy Who Died and Came Back (Novato CA: New World Library, 2014).
Journal drawing: "Make Me As Blue Sky" by Robert Moss