What do LDS believe was the purpose of the Tree of Life if Adam and Eve were created immortal?

We do not believe that Adam and Eve were meant to stay in the Garden of Eden. We believe that they were eventually meant to leave the garden and be subject to death. So, we believe that the Tree of Life represents God's love for all of us in providing a way by which we could be redeemed from the mortal state and have eternal life with our Heavenly Father. To be quite honest, I have problems seeing a purpose for the tree of life if Adam and Eve were supposed to stay in the Garden or were not supposed to be subject to death.

I have to DISAGREE with your above comment that adam and eve were not immortal and that they were created mortal.....That is INCORRECT DOCTRINE.
Adam and eve were created Spiritual meaning NO BLOOD =not mortal. President Joseph Fielding smith teaches this best in Doctrines of salvation

"Adams body was created from the dust of the earth but at the time it was a spiritual earth . Adam had a spiritual body until mortality came upon him through violation of the law which he was living, but he also had a physical body of flesh and bones.

Now what is a spiritual body? It is one that is quickened by spirit and not by blood. Our father in heaven and our savior and all those who have passed through the resurrection have physical bodies of flesh and bones but their bodies are quickened by spirit and not by blood hence they are spiritual bodies and not blood bodies. The immortal body is quickened by spirit, but the mortal body is quickened by blood. The lord said to Noah that blood is the life of the body in the mortal sphere (gen 9:4). also in D&C we have the following:
for notwithstanding they die, they also shall rise again a spiritual body. They who are of a celestial spirit shall receive the same body Which was a natural body {i.e. mortal body}; even ye shall receive your bodies and your glory shall be that glory by which your bodies are quickened.
....now when adam was in the garden of eden he was not subject to death. There was no blood in his body and he could have remained there forever. This is true of all other creations. This statement may not be pleasing to our evolutionists but it is true." (doctrines of salvation VOl 1 P. 76-77)

This is why the savior had to shed actual blood for the atonement and to make it possible to get back to a spiritual immortal body. because blood had entered into us by the fall and was the life of mortality/flesh

hope this helps

"Adam fell that men might be; and men are, that they might have joy." -- 2 Nephi 2:25 in the Book of Mormon. We believe that if Adam and Eve had partaken of the forbidden fruit, then they could not have have children or experienced mortality. We need to know misery in order to be happy. We need to know what wrong is, so we can choose the right. God's plan uses opposition to help us grow and develop.

Actually, Adam and Eve were not created immortal, they were very much mortal, but were in a translated state. The fruit of the tree of life kept them in that state while in the Garden of Eden.

It was only the tree of the knowledge of good and evil they were commanded not to partake. Look at what God says in Gen.3;22,23.."And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
23 Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken."

Had Adam or Eve partook of the tree of life before God came to them they would have ruined the Lord's plan for us completely. God had to remove them from the garden. It was necessary that Adam and Eve remain mortal to complete the Lord's plan...Later