First, let's consider what the Old Testament teaches about capital punishment prior to the flood.
While this period only covers the first six chapters in Genesis, chronologically it covers over 1600 years of history (cf. Gen. 5). In those first six chapters, we do have record of a couple murders (cf. 4:8,23). Though our information is very limited regarding Lamech, it is clear that in Cain's case the death penalty was not to be enforced by man (and it wasn't enforced by God). Cain was punished severely (as he saw it)--a life-sentence, if you will, but he was not put to death. In fact, God did not want Cain put to death (cf. 4:15). The only other recorded event that has any applicability here would be 2:17, which we alluded to previously. God originated the idea that certain sins are worthy of death as a penalty. One might also speculate that murder was one of the common problems alluded to in 6:5. Regardless, one thing seems clear at this point in history: God had given no instructions regarding the practice of capital punishment. There is no reason specifically revealed as to why this was the case. Some might suggest that this is because God never intended capital punishment to be implemented. I reject that notion, strictly because of what is revealed later in the Old Testament. God Himself does not change regarding His nature and character (cf. Mal. 3:6), though at various points in His dealings with humanity, His full will might not yet be revealed or it may even change from one dispensation to the next.
Second, let's consider what the Old Testament teaches about capital punishment after the flood but before the Law of Moses was revealed.
During the global deluge, God put to death (via the flood waters) every human being on Earth except eight souls (cf. I Pet. 3:20). I realize this is not an example of humans executing humans, but it does illustrate that God is sovereign and that certain sins can lead to the forfeiture of one's life (individually or even collectively, as we see here).
After the flood, God began requiring capital punishment. Genesis 9:3-6 reads:
"Every moving thing that lives shall be food for you. I have given you all things, even as the green herbs. But you shall not eat flesh with its life, that is, its blood. Surely for your lifeblood I will demand a reckoning; from the hand of every beast I will require it, and from the hand of man. From the hand of every man's brother I will require the life of man. Whoever sheds man's blood, by man his blood shall be shed; for in the image of God He made man."
This is God's first command to humans for capital punishment, but it is certainly not the last. Interestingly, this is where eating meat is first authorized by God, which was a change from the prior age.
We will continue this study in our next lesson.