it sounds simple enough to me that the tree of life sustained Adam and Even indefinitely, and they lost it in the Fall. Here's what i'm concerned about though: just because their lives were sustained by that tree, this doesn't necessarily imply that death was a natural or built-in part of Edenic/original creation, right? i can see why a person might be inclined to think so, but i really don't think that necessarily follows.
i know a lot of people might see this as just one among many novel curiousities we come up with regarding the Garden, but i really don't think this is as trite a matter as whethe or not Adam and Eve had belly buttons or how much time did they truly spend in Eden prior to the Fall. If we say that death was a natural part of God's original design, i think we rob the Bible of a lot of meaning that cries out to be understood.
First, the curse itself seems like less of a curse. If Adam and Eve would have died anyway, then why was it really a curse to be told they would die?
Second, Christ's resurrection is depleted of meaning. If death was a natural part of God's creation, then Christ's resurrection was little more than one premise in a syllogism about His divinity. i think Christ's resurrection clearly tells us something about His reversal of the curse, and also indicates that God intends to redeem all of creation from that curse.
Third, our own resurrections are depleted of meaning. i suspect that many people find bodily resurrection superfluous anyway, and that's why they (though professing Christians) don't really believe that they will be bodily raised from the dead, but will just have their disembodied spirits float around in an immaterial heaven forever. Or if they do believe in bodily resurrection, again, they see it almost as an ad hoc to God's plan for the end of the world. Our own bodily resurrections are significant for several reasons, but one of which is that our own bodies need redeemed from the effects of sin. To say that death was a part of the original creation implies that there's nothing our bodies really need redeemed from.
Fourth, so many passages in the NT speak of death as an enemy (ex, 1Cor 15). Death is not natural or normal, but is a nasty monster that needs conquered. The Pelagian idea that death is a natural, built-in part of God's original creation suggests that such passages are gross exaggerations.
Fifth, death is a nasty monster that was borne of human sin. If we claim that God through Christ sought to deal with sin, then physical death is part of that which needs dealt with.