i think your question is very interesting and i've been doing a little research on this. i'm not really sure what the answer is, but the bible is so interesting. The bible starts with the tree of life and with the cherubims guarding it with a flaming sword, so that men can no longer approach this tree of life and gain eternal life [Gen 3:24]. Now, the last chapter of the Bible talks about this tree of life that is unguarded and is accessible to everyone who is in the book of life for our healing [Rev 22:2].
Now, the thing that I note is interesting is that initially, we had the garden of Eden, out of which flowed a river [Genesis 2:10]. Now, in this new city, we see a river as well, but that is proceeding out of the throne of God and of the Lamb [Rev 22:1]
So, what is the difference? I think the key scripture here is in [Revelations 21:1-2]
1 And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea.
2 And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband.
So, this new city is a new city, old things are passed away. So I don't think it is the same tree because this new city has improved properties or value. This is a heavenly city, not an earthly one. The river flows not out of Eden, but out of the throne of God. So, therefore, I think (to me that is), this is a new tree of life with new properties that God has created anew. If the city is new and better, and the river is new and better, do u think that the tree is a new tree with improved properties that God has created for us to provide us with life everlasting?
Again, I am no theologian, this is only my own opinion. I am free to accept views from others.