Narrative analysis: The vision of the tree is a common element among the three visions we are examining, that of Lehi, Joseph Smith, Sr.,and the Narrative of Zosimus. The trees all serve as symbolic conduits for the divine, but do so in a slightly different way. In the vision of Lehi and Joseph Smith Sr., it is the fruit of the tree which becomes the ultimate communicator of the divine. In the narrative of Zosimus the trees are the mode of reaching another plane.
The use of tree of life symbolism is a world wide phenomenon, and the presence of the image in these visions is indicative of the wide ability of the tree to evoke the connection with the divine.
Symbolic analysis: Lehi does not overtly name the tree as the tree of life, though Nephi does in his personal version of the dream (1 Nephi 11:25). Nevertheless, Lehi could not fail to see the symbolic confluence of the tree and fruit in this dream and that of the tree in the Garden of Eden. Nevertheless, while the Edenic tree stands as the symbolic prototype, Lehi's vision is not a recurrence of the Garden imagery nor symbolism. As with much of Book of Mormon theology, Lehi's dream is more clearly prescient of Christ's role in the world, and theme which is much more deeply buried (albeit present) in the Garden's tree.
The verses do not make it clear how Lehi knows that the fruit is "desirable to make one happy", though it may be assumed that the knowledge came from the accompanying messenger. It is perhaps unfortunate that Joseph Smith chose the word "happy" here, because that word connotes too fleeting an emotion. It is more likely that this fruit provides the celestial emotions which are later translated as "joy".