Genesis 2:9 introduces us to the tree of life: “Out of the ground the Lord God made grow every tree that was delightful to look at and good for food, with the tree of life also in the middle of the garden and the tree of the knowledge of good and evil.” According to Genesis 2:16-17, God told Adam, “You are free to eat from any of the trees of the garden [evidently including the tree of life] except the tree of the knowledge of good and evil. From that tree you shall not eat; when you eat from it you shall die” — that is, become subject to death.
Why did God make Adam and Eve subject to this danger? For Adam and Eve’s wills to be free, there had to be the possibility of misusing them. Otherwise, our first parents would have been mere automatons.
The tempter, the father of lies, persuaded Eve (and through her, Adam) that eating the forbidden fruit would confer divine status on them. Indeed, the tempter spoke the truth, but with an entirely different, ominous meaning. By this act of disobedience, she and Adam certainly would know good and evil. But how? By themselves, actually becoming evil, disobedient to God.
Note that the fruit of the tree of life, which was believed to confer eternal life, was not forbidden to Adam and Eve not prior to their fall, but after their fall. Only then — and for Adam and Eve’s ultimate benefit — did God forbid them to eat the fruit of the tree of life (see Gn 3:22-24). In their condition of disobedience they would eternally have been cut off from God. It was an act of mercy for God to prevent them from plunging themselves into damnation. God had in mind the new Adam through which he would restore to the human race the possibility of eternal life lost in the fall of Adam and Eve.
What became of the tree of life after the fall? God drove out our first parents, “stationing the cherubim and the fiery revolving sword east of the garden of Eden, to guard the way to the tree of life” (Gn 3:24). Again, God took precaution against fallen humanity being eternally separated from Him. We know now the new Adam reopened the way to eternal life.