What were Laman and Lemuel's sins?

They did not believe their Father or Nephi could be a prophet. (1)

They did not believe they could receive revelation as Nephi claimed. (2)

They believed all was well in Zion, that the people of the church were a righteous people.(3)

They were slothful because they had no vision.  Who among us would put forth a great effort when the propriety of the course of action was in doubt?

They reject the testimony of Nephi; he was not a bona fide source of truth because he held no office, position or rank. (4)

Anger caused by pride and, no doubt, a feeling of righteous indignation led them to believe they were justified in killing Nephi and Lehi.

To Laman and Lemuel, Nephi was a wild man.

1. "Now, he says that the Lord has talked with him, and also that angels have ministered unto him. But behold, we know that he lies unto us; and he tells us these things, and he worketh many things by his cunning arts, that he may deceive our eyes..." (1 Nephi 16:38)

2. "And I said unto them: Have ye inquired of the Lord?  And they said unto me: We have not; for the Lord maketh no such thing known unto us. Behold, I said unto them: How is it that ye do not keep the commandments of the Lord? How is it that ye will perish, because of the hardness of your hearts?" (1 Nephi 15:8-10)

3. "And we know that the people who were in the land of Jerusalem were a righteous people; for they kept the statutes and judgments of the Lord, and all his commandments, according to the law of Moses; wherefore, we know that they are a righteous people; and our father hath judged them, and hath led us away because we would hearken unto his words; yea, and our brother is like unto him." (1 Nephi 2:12)

4. "And Laman said unto Lemuel and also unto the sons of Ishmael: Behold, let us slay our father, and also our brother Nephi, who has taken it upon him to be our ruler and our teacher, who are his elder brethren."