1 Nephi 3:10–12

10 And it came to pass that when we had gone up to the land of Jerusalem, I and my brethren did consult one with another.

11 And we cast lots—who of us should go in unto the house of Laban. And it came to pass that the lot fell upon Laman; and Laman went in unto the house of Laban, and he talked with him as he sat in his house.

12 And he desired of Laban the records which were engraven upon the plates of brass, which contained the genealogy of my father.

Apparently none of the brothers was all that excited about facing Laban to ask for the plates, otherwise there would have been volunteers. But instead they cast lots, a way to make a random choice. Interesting that the lot fell on Laman, who, being the oldest, should have been the volunteer. Was it coincidence that Laman was chosen? Maybe, but Proverbs 16:33 seems to indicate that the Lord has the final say about how the lot is cast. Either way we need to again give Laman credit here. He obviously didn’t want to go in the first place, but not only did he make the trip, he went in to Laban alone when the lot was cast in his favor. And I think he did the reasonable thing. He gave Laban the opportunity to do the Lord’s will first on his own accord.