When we approach the story we usually take note of Laman and Lemuel's failure to pray and identify with Nephi's apparent natural understanding about the role of prayer in revelation. But when we consider Nephi's reaction to his father's vision we have to keep in mind that not only are we reading it through our cultural lens, but also we are reading the version of the story that Nephi wrote many years later. By the time he wrote his story Nephi may have been much more comfortable with praying to receive knowledge through revelation, but it may not have been that way at the time.
We can deduce that there was one particular scripture that impacted how Nephi viewed revelation and prayer because he quoted it to Laman and Lemuel. In 1 Nephi 15:11 Nephi says,
"Do ye not remember the things which the Lord hath said?—If ye will not harden your hearts, and ask me in faith, believing that ye shall receive, with diligence in keeping my commandments, surely these things shall be made known unto you."This verse was evidently on the brass plates, but is not found in our Old Testament. We do not know when Nephi first encountered this verse, but it may have only been read by Lehi and his family just a few days before. In retelling this story many years later, Nephi carefully incorporates this verse into his exchange with his brothers (see how verse 10 sets up how verse 11 applies to the situation). But at the time Nephi may have only recently learned of that verse, and much like Joseph Smith with James 1:5, took it seriously. The same verse may not have had the same impact, or even been noticed by Laman and Lemuel.
But in 1 Nephi 11:20-21, Nephi mentions that his brothers were humbled and began to ask sincere questions. They must have found that verse convincing, but that would also mean that they were not familiar with it, so Nephi must have also just learned that verse when they acquired the brass plates.
So why did Nephi pray? He did it because he read the scriptures and found out that he could. It is "obvious" to us now, and it was obvious to Nephi later in life, but at the time it was a new thing.