According to Brant Gardner, the use of lots to determine who should go up to Laban now raises another question. If the Lord did have a hand in the selection, why was Laman chosen instead of Nephi? Clearly the Lord knew that Nephi would be the successful one. . . . Why would the Lord put Laman in a position where the Lord knew he would fail?
The incident of the retrieval of the brass plates comes directly after Nephi's epiphany wherein the Lord told Nephi that he would ascend over his brothers. While that had occurred in other historical occasions (Jacob over Esau, Joseph over all his brethren) it was remarkable in its violation of cultural rules. For the eldest brother was the one who should have that role.
The incident with the brass plates is a transitional moment where the change in the leadership hierarchies is being established. The Lord uses this incident to provide justification for the ascendancy of Nephi as a leader, a process which continues on their journey through the desert. Laman's attempt and failure was both a recognition of his birthright, and the marking of the passage of the birthright from the inheritor to the more righteous anointed. [Brant Gardner, "Brant Gardner's Page, Book of Mormon Commentary, [http://www.highfiber.com/~nahualli/LDStopics/] 1Nephi/1Nephi3.htm, pp. 4-5]
Note* The reader should note that the birthright we should be focusing on is the covenant birthright, which of necessity is based on covenant obedience. Nephi was more than just good or righteous, he had personally covenanted with the Lord and was being faithful to that covenant (see 1 Nephi 2:16-24). Laman failed to be obedient to those covenant obligations; Nephi was obedient. [Alan C. Miner, Personal Notes]