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According to Lucy Mack Smith, Joseph Smith, Senior, the father of the Prophet, had the following dream in 1811 when the family was living in Lebanon, New Hampshire. Joseph Smith, Junior, would have been 5 years old at the time. I thought...I was traveling in an open, desolate field, which appeared to be very barren. As I was thus traveling, the thought suddenly came into my mind that I had better stop and reflect upon what I was doing, before I went any further. So I asked myself, "What motive can I have in traveling here, and what place can this be?" My guide, who was by my side, as before, said, "This is the desolate world; but travel on." The road was so broad and barren that I wondered why I should travel in it; for, said I to myself, "Broad is the road, and wide is the gate that leads to death, and many there be that walk therein; but narrow is the way, and straight is the gate that leads to everlasting' life, and few there be that go in thereat." Traveling a short distance farther, I came to a narrow path. This path I entered, and, when I had traveled a little way in it, I beheld a beautiful stream of water, which ran from the east to the west. Of this stream I could see neither the source nor yet the termination; but as far as my eyes could extend I could see a rope running along the bank of it, about as high as a man could reach, and beyond me was a low, but very pleasant valley, in which stood a tree such as I had never seen before. It was exceedingly handsome, insomuch that I looked upon it with wonder and admiration. Its beautiful branches spread themselves somewhat like an umbrella, and it bore a kind of fruit, in shape much like a chestnut bur, and as white as snow, or, if possible whiter. I gazed upon the same with considerable interest, and as I was doing so the burs or shells commenced opening and shedding their particles, or the fruit which they contained, which was of dazzling whiteness. I drew near and began to eat of it, and I found it delicious beyond description. As I was eating, I said in my heart, "I can not eat this alone, I must bring my wife and children, that they may partake with me." Accordingly, I went and brought my family, which consisted of a wife and seven children, and we all commenced eating, and praising God for this blessing. We were exceedingly happy, insomuch that our joy could not easily be expressed. While thus engaged, I beheld a spacious building standing opposite the valley which we were in, and it appeared to reach to the very heavens. It was full of doors and windows, and they were filled with people, who were very finely dressed. When these people observed us in the low valley, under the tree, they pointed the finger of scorn at us, and treated us with all manner of disrespect and contempt. But their contumely we utterly disregarded. I presently turned to my guide, and inquired of him the meaning of the fruit that was so delicious. He told me it was the pure love of God, shed abroad in the hearts of all those who love him, and keep his commandments. He then commanded me to go and bring the rest of my children. I told him that we were all there. "No," he replied, "look yonder, you have two more, and you must bring them also." Upon raising my eyes, I saw two small children, standing some distance off. I immediately went to them, and brought them to the tree; upon which they commenced eating with the rest, and we all rejoiced together. The more we ate, the more we seemed to desire, until we even got down upon our knees, and scooped it up, eating it by double handfuls. After feasting in this manner a short time, I asked my guide what was the meaning of the spacious building which I saw. He replied, "It is Babylon, it is Babylon, and it must fall. The people in the doors and windows are the inhabitants thereof, who scorn and despise the Saints of God because of their humility."

I soon awoke, clapping my hands together for joy.[

There are three potential explanations:

Joseph Smith plagiarized Joseph Sr.'s dream when he wrote the Book of Mormon. This is the stance adopted by the critics.
Joseph Sr. had a dream that was similar to the dream experienced by Lehi, and this was a sign to the Prophet's family that he was translating a real record that came from God. This is certainly possible, though it is impossible to prove or disprove by historical techniques, and so will not be elaborated on. It remains, however, a viable option.
Lucy Mack Smith's account of the dream (which she recorded many years after the fact, when the Book of Mormon account was well-known and published) may have influenced how she remembered and/or recorded her account of Joseph Sr's dream.

inquiringmind wrote:Does anybody know what Lucy actually wrote about the circumstances of this dream, and her husbands sharing of it?