What is the Biblical basis for Mary being the Tree of Life? The following is taken from True Devotion to Mary by St. Louis de Montfort:

If Mary, the Tree of Life, is well cultivated in our soul by fidelity to this devotion, she will in due time bring forth her fruit which is none other than Jesus.

In light of Genesis 3:22-24:

Then the LORD God said, “Behold, the man has become like one of us in knowing good and evil. Now, lest he reach out his hand and take also of the tree of life and eat, and live forever—” therefore the LORD God sent him out from the garden of Eden to work the ground from which he was taken. He drove out the man, and at the east of the garden of Eden he placed the cherubim and a flaming sword that turned every way to guard the way to the tree of life.

Since God's clear intent was to prevent man from eating of the tree of life, what is the biblical basis for Mary being the Tree of Life and Jesus the fruit thereof?
What is the Biblical basis for Mary being the Tree of Life?
This is a metaphor for Mary. Christ is the source of our salvation and our eternal life. Mary is the one that bore Jesus into the world. Thus Mary is the Tree that produced the Fruit which (who) is no other than Jesus of Nazareth, who is called the Christ!
Catholics believe in the Eucharist! Thus Jesus is the fruit. Mary is the tree of life that produced the God-Man, who in turn gave us his flesh to eat at the Last Supper.
For a biblical basis, I would recommend St. Like’s narrative on the birth of Jesus:

The Birth of Jesus
2 In those days Caesar Augustus issued a decree that a census should be taken of the entire Roman world. 2 (This was the first census that took place while[a] Quirinius was governor of Syria.) 3 And everyone went to their own town to register.
4 So Joseph also went up from the town of Nazareth in Galilee to Judea, to Bethlehem the town of David, because he belonged to the house and line of David. 5 He went there to register with Mary, who was pledged to be married to him and was expecting a child. 6 While they were there, the time came for the baby to be born, 7 and she gave birth to her firstborn, a son. She wrapped him in cloths and placed him in a manger, because there was no guest room available for them.
8 And there were shepherds living out in the fields nearby, keeping watch over their flocks at night. 9 An angel of the Lord appeared to them, and the glory of the Lord shone around them, and they were terrified. 10 But the angel said to them, “Do not be afraid. I bring you good news that will cause great joy for all the people. 11 Today in the town of David a Savior has been born to you; he is the Messiah, the Lord. 12 This will be a sign to you: You will find a baby wrapped in cloths and lying in a manger.”
13 Suddenly a great company of the heavenly host appeared with the angel, praising God and saying,
14 “Glory to God in the highest heaven,
and on earth peace to those on whom his favor rests.”
15 When the angels had left them and gone into heaven, the shepherds said to one another, “Let’s go to Bethlehem and see this thing that has happened, which the Lord has told us about.”
16 So they hurried off and found Mary and Joseph, and the baby, who was lying in the manger. 17 When they had seen him, they spread the word concerning what had been told them about this child, 18 and all who heard it were amazed at what the shepherds said to them. 19 But Mary treasured up all these things and pondered them in her heart. 20 The shepherds returned, glorifying and praising God for all the things they had heard and seen, which were just as they had been told.
21 On the eighth day, when it was time to circumcise the child, he was named Jesus, the name the angel had given him before he was conceived. - Luke 2