Doctrinal analysis (verse 18): In verse 18 Nephi grieves over the inability of Laman and Lemuel to believe his words as Sam did. Nephi does not leave it at that, however, and returns to the Lord to pray for his brothers. Thus should we also continually turn to the Lord over our loved ones.
Nephi's preaching to his brethren also establishes the mission of the family from a second source, and complies with the word of God coming from two or more witnesses ( Deuteronomy 17:6).
Redactive analysis: Nephi's confirmation from the Lord that his father's actions are divinely inspired (verse 16) are followed directly by a second witness from the Lord. While Nephi may have had other prayers answered prior to these events, we do not know of them. In fact the confirming witness which Nephi communicates to Sam has only one narrative function, and that is to set up the conditions for Nephi's first major revelation described in the text of the Book of Nephi. When Nephi cannot convince Laman and Lemuel as he did Sam, Nephi returns to the Lord. What Nephi receives at this time is his prophetic calling, and the divine validation of the social restructuring of the family affairs. Not only is Nephi called as a prophet (verses 19 and 20 - note that the Lord now specifically mentions leading Nephi to the land of promise - it does not say that Lehi would be led....)but Nephi is told that he will have political ascension over his brothers (verse 22). This is contrary to traditional law, and places Nephi in a similar context to Joseph of old (from whom he is descended) in that the younger brother has visions from the Lord, and eventually alters the traditional family position rules.
Scriptural analysis (verses 19-24): Nephi's prophetic calling does not come without any preparation on Nephi's part. In verse 19 we see Nephi as a man of faith, who has sought the Lord diligently. Nephi possesses the faith and lowliness of heart to use his faith. He also does so for the benefit of others, not simply for selfish motives.
Verse 20 implicitly calls Nephi to be the prophet of the exodus to the New World. Indeed, from this point in the narrative on, Lehi's role diminishes and Nephi's increases. In this context it interesting to note that the first indication of the ultimate destination of the family's journey comes to Nephi, not Lehi, if our indications are correct from the text as we have it. It may be that Lehi knew, but there is no evidence of it in the current Book of Mormon.
Since the purpose of Nephi's inquiry to the Lord is to plead for Laman and Lemuel, he receives information about them. It was not the hopeful information that Nephi had probably desired. The Lord does not instruct Nephi on the methods of converting his brethren. There is no "tell them to go and wash seven times in the river Jordan" (see 2 Kings 5:10-14). Nephi is rather clearly told that should his brethren rebel, they should be cut off.
The lack of hope in that statement continues with the predictions that Nephi will rule over his brethren, and the description of a long-lasting feud between his and his brothers lineages (v 24 "they shall be a scourge unto they seed...).