ok, so be patient with me here. i am not a programmer so my logic skills might not be as razor sharp as yours....
so, if the first death was mortality, then why were they also prevented from eating of the tree of life?
to me, it seems that Adam was told he would return to the dust. is this not the same thing as mortality?
and, when God told them that if they ate the fruit, they (both of them) would die (mortality).
they ate, they became mortal. THEN, they are also prevented from eating of the tree of life.
i'm confused here.
Quoting: Salt 
Only Adam was forbidden to eat of the Tree of Life (abbrev. ToL), and it was because he alone rebelled to the point of blaming God for his sin. Eating of the ToL would be required due to their mortality as a result of both of them eating from the Tree of the Knowledge of Good and Evil (abbrev. TKGE).
As for mortality and returning to dust, you may be wondering how this could apply to Eve who had never been dust. We aren't told what state Eve would have "returned" to had she somehow stayed in the garden yet did not eat of the ToL. But it seems absurd to think she would not have eaten of the ToL, so it's likely a moot point.
All we get from the text is that "in the day you eat of it, you will surely die", without any more detail as to what "surely die" meant. We can only note that eating of the ToL would be the antidote, and I have a hard time accepting that spiritual life can come from eating fruit.
So they became mortal (able to die), and would need to eat of the fruit of the ToL to prevent the inevitable actual death.
Mortality is the ability, not the end result. Adam and Eve thus had the possibility of dying, whereas before sin they did not. Contrast this with "immortal"; it means "cannot die", not simply "is alive". Does that help?
