In order to explore this question, I first want to address several aspects of ancient Judaism. I believe it is safe to say that Nephi was fairly familiar with many aspects of Judaism at the time of his life. There are several things that make me think this. One being the state of Lehi and his families living conditions. It is made fairly obvious that his family was rich. The reasons can vary for this, but truthfully, there were little stations in life at the time that could bring about true wealth. While some, like Hugh B. Nibley, argued that Lehi was likely a merchant in the city, I feel the issue of importance is not what Lehi did, but that he had wealth; enough to make Laban willing to kill or capture Lehi's sons for the treasures (1 Ne. 3:26). This wealth can then easily be associated with intellectual learning, a large part of this learning being of their scripture. Furthermore, Lehi knowing about the brass plates helps to indicate his access to that type of information.
So what laws, etc. would Nephi have been aware? Well, any, if not all of this is speculative (which causes some real issues in ultimately answering our big question), and must remain speculative in order to come to some type of understanding of how Nephi could have addressed the killing of Laban.
Starting with Laban's treatment of the four brothers, we see malicious attempts to capture them. What he intended to do with them is of not much importance as the consequence (as I read it) for such actions are ultimately the same: death (Exodus 21:16). In this scripture, we learn that enslaving another man is punishable by Jewish law by death. I have seen some accounts attribute Exodus 22:2 as justification for killing one who robs you, but the scripture is misinterpreted. The justification lies and not recognizing your robber at night. If you defend yourself and property at that moment, it is, according to Exodus, not a crime.
However, we see many examples where laws, requiring the eradication of evil and sometimes using violent means, exist in the Jewish tradition. We see in 2 Sam. 20:1 Sheba, the Israelite, rebelling against David, leading tribes away (an interesting comparison to the "dwindle in unbelief" idea). For this, Sheba was beheaded.
We also find scriptures saying, "I the LORD have spoken" (Ez. 24:14) indicating a finality to what God says--he has the final word.
It may also be worthwhile to look at the Babylonian influence at the time of Nephi's life. While it may not have had much impact on his belief system, the culture he is ingrained in (much like today) would have to have an effect on his perceptions. During these times, perceptions of death were met greatly with no judgment for the good or bad. All received a common fate. This can have a powerful effect on Nephi's Judaism beliefs, especially regarding an ambiguous understanding of the afterlife (presumably at this time in his life).
Each of the cultural beliefs and commonalities, I feel would have been known by Lehi, and, therefore, presumably Nephi. Again, whether it had an effect on his understanding of death and killing cannot be known, but through his actions, I believe we can make certain assumptions of how things in his mind may have played out. In the third installment of this topic, I will show a comparison to these beliefs to Nephi's actions to hopefully shed some further light on why Nephi killed Laban.