"In that same year there came many prophets, prophesying unto the people that they must repent, or the great city Jerusalem must be destroyed. Wherefore it came to pass that my father, Lehi, as he went forth prayed unto the Lord, yea, even with all his heart, in behalf of his people. And it came to pass as he prayed unto the Lord, there came a pillar of fire and dwelt upon a rock before him; and he saw and heard much; and because of the things which he saw and heard he did quake and tremble exceedingly." (1 Ne. 1:4-6)Lehi seems to believe the words of the prophets, for he prays for and in behalf of the wicked people. I would guess that he's been aware of the wickedness of his people, and he might have waited for God's warning to be proclaimed.
It's hard to show from the text that Lehi was seeking for more knowledge than what he had received from the prophets. Still, the Lord showed him great things.
The power of the intercessory prayer can't be underestimated, nor can the power of believing the words of God's real prophets.
Lehi's approach is that of belief in the words of others. A seemingly functional way to approach the word of God.
Laman and Lemuel
"Now this he spake because of the stiffneckedness of Laman and Lemuel; for behold they did murmur in many things against their father, because he was a visionary man, and had led them out of the land of Jerusalem, to leave the land of their inheritance, and their gold, and their silver, and their precious things, to perish in the wilderness. And this they said he had done because of the foolish imaginations of his heart. And thus Laman and Lemuel, being the eldest, did murmur against their father. And they did murmur because they knew not the dealings of that God who had created them. Neither did they believe that Jerusalem, that great city, could be destroyed according to the words of the prophets. And they were like unto the Jews who were at Jerusalem, who sought to take away the life of my father. […] But, behold, Laman and Lemuel would not hearken unto my words; and being grieved because of the hardness of their hearts I cried unto the Lord for them." (1 Ne. 2:11-13, 18)Laman and Lemuel disbelieves in the words of the prophets, they are stiffnecked and hardhearted, they call Lehi foolish and they murmur (because they knew not God). This is the opposite approach, the one of dis- and unbelief. Despite this, they left Jerusalem (and returned twice without staying there).
"And it came to pass that I, Nephi, being exceedingly young, nevertheless being large in stature, and also having great desires to know of the mysteries of God, wherefore, I did cry unto the Lord; and behold he did visit me, and did soften my heart that I did believe all the words which had been spoken by my father; wherefore, I did not rebel against him like unto my brothers." (1 Ne. 2:16)The text doesn't fully describe Nephi's intents and what he said in his cry unto the Lord, but it seems that he didn't go to the Lord for confirmation that his father spoke the truth. Instead, he went to the Lord to learn of His mysteries for himself. In my mind, there's a big difference in this. Instead of just "feeling good" about the direction his father was leading the family, Nephi gained great knowledge and got his own promises from the Lord. Nephi seeks a first-hand experience!
"And I spake unto Sam, making known unto him the things which the Lord had manifested unto me by his Holy Spirit. And it came to pass that he believed in my words." (1 Ne. 2:17)Nephi tells Sam about his (Nephi's) experience (which confirms that of Lehi). Sam believes the testimony of Nephi. This experience and this belief seems to have sent Sam on his own journey to the presence of Christ, for later, Lehi blesses Sam with these words (it should also be noted that Sam, later in the Book of Mormon, is called a just and holy man; see Alma 3:6):
"And after he had made an end of speaking unto them, he spake unto Sam, saying: Blessed art thou, and thy seed; for thou shalt inherit the land like unto thy brother Nephi. And thy seed shall be numbered with his seed; and thou shalt be even like unto thy brother, and thy seed like unto his seed; and thou shalt be blessed in all thy days." (2 Ne. 4:11)Sariah
"For she had supposed that we had perished in the wilderness; and she also had complained against my father, telling him that he was a visionary man; saying: Behold thou hast led us forth from the land of our inheritance, and my sons are no more, and we perish in the wilderness. And after this manner of language had my mother complained against my father. And when we had returned to the tent of my father, behold their joy was full, and my mother was comforted. And she spake, saying: Now I know of a surety that the Lord hath commanded my husband to flee into the wilderness; yea, and I also know of a surety that the Lord hath protected my sons, and delivered them out of the hands of Laban, and given them power whereby they could accomplish the thing which the Lord hath commanded them. And after this manner of language did she speak." (1 Ne. 5:2-3, 7-8)Sariah must have had a hard time leaving Jerusalem and then letting her sons go back to get the plates. It seems that she fully believed once she'd seen physical evidence of the Lord's hand in preserving her sons. Still, she must've had some kind of desire to believe, for she went with her husband into the wilderness.
We choose how to approach the words of God. Either we believe the words of others, we disbelieve, we believe after getting "proof", or we seek our own knowledge of the mysteries of God. Let's choose wisely.