Good question. Before the sin of listening to the bad advice of the snake, God did not forbid eating from the Tree of Life. In fact, it is described as being "in the middle of the garden", in a central and convenient place to go. Had they eaten from it they could have been immortal.
In a sense, Adam and Eve, before the sin were neither mortal nor immortal. When they sinned their reality was determined as mortal, but had they not sinned and eaten of the Tree of Life their reality would have been determined as immortal.
Interestingly, the Tree of Life is guarded by Cherub angels, and the only other item in the Torah that was “guarded” by Cherub angels is the Holy Ark. The Ark (Aron) which contained the Torah was covered by two Cherubs. The Torah is also called a "Tree of Life".
However, unlike Adam and Eve who lost immortal life through their sin, the Jewish People who sinned with the Golden Calf were nevertheless allowed to partake of the Torah — the Tree of Life. Through the study and fulfillment of Torah, we can achieve clarity of reality and a purity of existence that theoretically makes suffering, and even death unnecessary, and allows the human being to achieve a close and immortal relationship with the Creator, despite having eaten from the Tree of Knowledge.
