Genesis 5:29 cites the words of Noah's father Lamech. The words themselves point back to the words of God in Genesis 3:15-19. These verses speak of the curse that God put on the ground and the endless toil that would ensue in order to get the ground to produce food. These verses also set up a solution to the problem: the arrival of the offspring of the woman who would defeat the Serpent and lift the curse from the ground. This was the great expectation from the very beginning: who would be that person?
When Eve was about to give birth to Cain she said as recorded in Genesis 4:1,
“I have gotten a man with the help of the LORD.”
Cain, of course, killed Abel and received an added curse: In Genesis 4:11–12 we see God's decree to Cain:
"And now you are cursed from the ground, which has opened its mouth to receive your brother's blood from your hand. When you work the ground, it shall no longer yield to you its strength. You shall be a fugitive and a wanderer on the earth.”
He obviously was not the one prophesied to lift the curse!
As Eve gave birth to her next child after Abel she also alluded to that expectation:
"And Adam knew his wife again, and she bore a son and called his name Seth, for she said, “God has appointed for me another offspring instead of Abel, for Cain killed him.” (Genesis 4:25)
The search for the deliverer who would bring rest to a weary world continued. We can presume that this expectation continued with each of the descendants of Eve all the way to Noah.
This then explains the words of Noah's father, Lamech.
“Out of the ground that the LORD has cursed, this one shall bring us relief from our work and from the painful toil of our hands.”
His expectation was that his son Noah would bring rest to a tired humanity and would lift the curse from the ground. Noah came very close to being that person considering that those that listened to his preaching and obeyed were saved from the flood. But in the end he, like all the rest of humanity, fell into sin, thereby disqualifying himself from being the fulfillment of the prophecy of Genesis 3:15.