What is the Biblical basis for Mary being the Tree of Life?
Mary Visits Elizabeth
41When Elizabeth heard Mary’s greeting, the baby leaped in her womb, and Elizabeth was filled with the Holy Spirit. 42 In a loud voice she exclaimed, “Blessed are you among women, and blessed is the fruit of your womb! 43And why am I so honored, that the mother of my Lord should come to me? - Luke1:41-43
Scriptures says, no one can say Jesus is Lord unless one received the gifts of the Holy Spirit. St. Elizabeth was filled with the Holy Spirit and she now understand and can proclaim the Truth, that what Mary bears in Her womb was Jesus, His Lord.
3Therefore I inform you that no one who is speaking by the Spirit of God says, “Jesus be cursed,” and no one can say, “Jesus is Lord,” except by the Holy Spirit. - 1Corinthian12:4
To give a clear understanding biblically of your cited teachings coming from St. Louis de Montfort regarding the Tree of Life and pointing to Jesus as the fruit and connecting it to Genesis passages in:
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.
The highlighted portion speaks of the Holy Eucharist, Jesus is the fruit, and anyone who eats Jesus will have eternal life and live forever. This passages speaks of the "Bread of Life" and also explain that the fallen man must work the ground, related to this passage:
Do not work for food that perishes but for the food that endures for eternal life, which the Son of Man will give you. For on him the Father, God, has set his seal.”
bSo they said to him, “What can we do to accomplish the works of God?”
Jesus answered and said to them, “This is the work of God, that you believe in the one he sent.” - John6:27-29
After we professed our faith that we believed in Jesus, we must be also filled with the Holy Spirit like St. Elizabeth, so that we not only believed in Jesus but we can also proclaim Jesus as our Lord and Saviour. And the most important thing is to eat the fruit that can give us eternal life to live forever in the Kingdom of God.
I am the living bread that came down from heaven; whoever eats this bread will live forever; and the bread that I will give is my flesh for the life of the world.” - John6:51
In Genesis3:22-24, after the fall of Adam and Eve, they were expelled and prevented from eating the fruit of the Tree of Life, in Catholic teachings the fruit or in the Bread of Life doscourse, it is the Holy Eucharist, and it is a sacrilege to receive and eat it, if we had committed a mortal sin, like Adam & Eve who had committed a mortal sin, they cannot eat the fruit, they must "work the ground" first. The meaning of "work the ground" is to do penance and Adam and Eve must see the promised Saviour.
In closing, Mary is the Tree of Life and Jesus is the fruit, we need to go the Tree in order to have Jesus the fruit. We cannot ignore the Tree of Life, which is Mary the Mother of Jesus Christ. And this can be found in Catholic famous prayer the Hail Mary;
"...and blessed is the fruit of thy womb, Jesus."
And the fruit, is the bread of life or the Holy Eucharist. And by eating the fruit, all who see and believe in Jesus Christ can have eternal life. But if we want to do more for God, this time by proclaiming our faith in Jesus Christ, we all need first to be "filled with the Holy Spirit", because we can only say Jesus is Lord if we had received the fullness of the gifts of the Holy Spirit.