Two things.
1) They did not eat from the Tree of Life. God removed them from the garden to prevent it.
Only After they had eaten from the tree of the knowledge of good and evil where they removed from the garden.. Before that time they had access to every tree in the garden Except for the tree of the knowledge of good and evil..
Genesis 2: KJV
16 "And the LORD God commanded the man, saying,
Of every tree of the garden thou mayest freely eat: {17}
But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die."
So the tree of Life was in the Garden and God told them they could eat of every tree in the garden except 1.. the tree of the knowledge of good and evil.. So Adam and Eve where free to eat of the tree of life..
Genesis 2: KJV
9 "And out of the ground made the LORD God 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 knowledge of good and evil."