How did the tree of life in the Garden of Eden serve its purpose? (Roman Catholic perspective)

In Genesis 2:9 (RSVCE) we read: > And out of the ground the Lord God made to grow every tree that is pleasant to the sight and good for food, the tree of life also in the midst of the garden, and the tree of the knowledge of good and evil. We further read in Genesis 3:2-3: > And the woman said to the serpent, “We may eat of the fruit of the trees of the garden; but God said, ‘You shall not eat of the fruit of the tree which is in the midst of the garden, neither shall you touch it, lest you die.’” My question is: How did the tree of life serve its purpose, if Adam and Eve were forbidden from eating its fruit? Are any teachings from the side of Catholic Church available on the topic?