In Genesis 4:23-24, Lamech said to his wives that "If Cain shall be avenged sevenfold, truly Lamech seventy and sevenfold." What is the point of this message? It is what Lamech said, instead of being from God. So should we understand the statement in Genesis 4:24 as having no authority at all?
In Genesis 4:26, "then began men to call upon the name of the Lord". May I know what it means by "call upon the name of the Lord" here?
Much of the Bible teaches us through stories of what happened. By our observing how people behaved, we learn more about how we ought to behave.
"Then Lamech said to his wives: "Adah and Zillah, hear my voice; Wives of Lamech, listen to my speech! For I have killed a man for wounding me, even a young man for hurting me. If Cain shall be avenged sevenfold, then Lamech seventy-sevenfold"" (Genesis 4:23-24).
Not only was Lamech a polygamist, giving us a hint at how fast sin crept into society after the creation, but his statement tells us that he was arrogant and unrepentant over the murder he did in vengeance. Notice that he justifies murdering a young man because he hurt Lamech in some way. Lamech is actually proud of his murder and thinks that if anyone should come after him for his deed that their punishment should be 77 times as severe. After all, Cain was protected by God (Genesis 4:15), so Lamech thinks he deserves even greater protection.
See this, so soon after the perfection of creation, the severe immorality of the world 1600 years after creation doesn't surprise us nearly as much. "Then the LORD saw that the wickedness of man was great in the earth, and that every intent of the thoughts of his heart was only evil continually" (Genesis 6:5).
So the statement of the evil Lamech carries no authority, but it gives us insight into the times in which Lamech lived and tells us a great deal about his character.
"And as for Seth, to him also a son was born; and he named him Enosh. Then men began to call on the name of the LORD" (Genesis 4:26).
The name of someone is their authority. Peter was asked, "By what power or by what name have you done this?" (Acts 4:7). His response was, "let it be known to you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom you crucified, whom God raised from the dead, by Him this man stands here before you whole" (Acts 4:10). Who gave Peter the authority or right to heal a man? Peter said it was by Jesus's authority. See "All in a Name" for more on a this matter.
To call on a name is to appeal to the authority of someone. The president of a country carries a lot of authority, so when he says something, people tend to listen. But you will also find people saying, "We need to do this because the President said it was important." In other words, the force of what they are saying isn't in themselves but in the name (reputation or authority) of someone else. In referring to someone else's authority, they are calling on his name.
You can see this in Peter's sermon. He quoted from the Old Testament, "and it shall come to pass that whoever calls on the name of the Lord shall be saved" (Acts 2:21). When asked what they needed to do to be saved, Peter said, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit. For the promise is to you and to your children, and to all who are afar off, as many as the Lord our God will call" (Acts 2:38-39). Repenting and being baptized was calling on the name of the Lord. "And now why are you waiting? Arise and be baptized, and wash away your sins, calling on the name of the Lord" (Acts 22:16). Believing, repenting, and being baptized doesn't, in itself, save people. It is because God said to believe, repent, and be baptized that those who do so are appealing to the authority of God for salvation.
So what Genesis 4:26 is saying is that beginning in the days of Enosh, not only was the world getting very corrupt, but there were also people who began to appeal to God for authority in what to do. People began to take sides between wickedness and righteousness. One of Enosh's descendants was the opposite of those Lamech represented. "And Enoch walked with God; and he was not, for God took him" (Genesis 5:24).