Lehi's exposition of Satan is brief, because it is not his point. Lehi's point is the importance of the events of the Garden, and Satan played a role there, but Lehi is not interested in any more than the briefest recounting of Satan - only sufficient to tell the story. Nevertheless, he does provide hints that he had a deep understanding of Satan beyond what we have in the scriptures from Lehi's time. Most interesting is Lehi's analysis that because Satan had "become miserable forever, he sought also the misery of all mankind." This statement should be seen in the context of Lehi's discourse on opposition, for we are still in a section of that tightly argued discourse.
Remember Lehi's delineation of opposition: "2 Nephi 2:11 For it must needs be, that there is an opposition in all things. If not so, my first-born in the wilderness, righteousness could not be brought to pass, neither wickedness, neither holiness nor misery, neither good nor bad. Wherefore, all things must needs be a compound in one; wherefore, if it should be one body it must needs remain as dead, having no life neither death, nor corruption nor incorruption, happiness nor misery, neither sense nor insensibility."
Twice in that verse Lehi uses misery as an opposite, first for holiness and second for happiness. In the context of Lehi's concerns, holiness and happiness must be seen as transcendental states, and happiness would be more than an ephemeral earthly feeling. For Lehi, these are parts of the eternal realm promised to us. When he contrasts that with misery, once again he refers to more than a temporary unhappiness. Satan is miserable not because he is unhappy, but because he is contrary to righteousness, contrary to holiness. He is miserable in contrast to the happiness and joy that are denied him.
It is interesting that it is in the context of Satan's misery and desire for our misery that Lehi places Satan's temptation of Eve. The clear implication is that Satan is tempting Eve to do something that should not be done, even though Lehi clearly understands the importance of the choice that will be made in the Garden. In Lehi's view, then Satan's misunderstanding of God's plan was sufficient than he did not understand it even so well as to understand that he was actually moving the plan forward rather than hindering it. In this Lehi follows a long tradition of seeing the Fall as bound up with sin, a viewpoint that only more modern revelation has begun to temper.
It is also interesting that Lehi presents Satan as the Father of all lies, and then has him telling Eve that they should not die, but rather become as the Gods, knowing good and evil. Certainly Lehi's point in this discourse is to show the essentiality of the latter promise. In that Satan did not lie. In his first promise, however, there is prevarication. While it is true that they do not die on that day, death is part of the deal, and Satan does not make the ramifications of partaking the fruit as clear as they should be. Perhaps it is even more to Eve's credit that she was able to reason out the importance of the action with such veiled information.