Genesis 3:17-24World English Bible (WEB)17 To Adam he said,
and ate from the tree,
about which I commanded you, saying, ‘You shall not eat of it,’
the ground is cursed for your sake.
You will eat from it with much labor all the days of your life.
18 It will yield thorns and thistles to you;
and you will eat the herb of the field.
19 By the sweat of your face will you eat bread until you return to the ground,
for out of it you were taken.
For you are dust,
and to dust you shall return.”
22 Yahweh God said, “Behold, the man has become like one of us, knowing good and evil. Now, lest he reach out his hand, and also take of the tree of life, and eat, and live forever...” 23 Therefore Yahweh God sent him out from the garden of Eden, to till the ground from which he was taken. 24 So he drove out the man; and he placed cherubim at the east of the garden of Eden, and a flaming sword which turned every way, to guard the way to the tree of life.
The lamb's blood over the door posts resembled the blood of Christ of whom has been referred to as the "Lamb of God" in the New Testament.
If you look at Revelation 2:7 the "Tree of Life" is welcomed:
7 He who has an ear, let him hear what the Spirit says to the assemblies. To him who overcomes I will give to eat of the tree of life, which is in the Paradise of my God.
The commonality of Genesis 3:22 and Revelation 2:7 is that when Adam and Eve were in their fallen state God kicked them out of the Garden of Eden because
1. They disobeyed and that led to their fallen state
2. He knew that they would partake of that which the Tree of Life produced, but because they were in a fallen state God did not want them to live forever within it.
II Timothy 1:10
8 Therefore don’t be ashamed of the testimony of our Lord, nor of me his prisoner; but endure hardship for the Good News according to the power of God, 9 who saved us and called us with a holy calling, not according to our works, but according to his own purpose and grace, which was given to us in Christ Jesus before times eternal, 10 but has now been revealed by the appearing of our Savior, Christ Jesus, who abolished death, and brought life and immortality to light through the Good News.
Jesus brings life and immortality...
1 He showed me a*n1 river of water of life, clear as crystal, proceeding out of the throne of God and of the Lamb, 2 in the middle of its street. On this side of the river and on that was the tree of life, bearing twelve kinds of fruits, yielding its fruit every month. The leaves of the tree were for the healing of the nations. 3 There will be no curse any more. The throne of God and of the Lamb will be in it...
"The throne of God and of the Lamb will be in it..."
There seems to be striking similarities between Jesus and this tree. The tree represents Jesus and what He brings to His true disciples.
Ultimately Adam and Eve were kicked out of the Garden for their disobedience. Had it not been for their disobedience their eyes wouldn't have been opened to good and evil. Today because of fallen nature our hearts are "...deceitful above all things, and it is exceedingly corrupt..." (Jeremiah 17:9)
So God preventing Adam and Eve from partaking in the fruit of the Tree of Life was actually a decision of mercy on behalf of their actions that led to their fallen status. If they were to live forever then they would be living forever in sin and immorality; but we have Jesus: the bread of life and living water who is the Tree of Life who provided the way to eternal life.