If we recall that the narratives in Genesis were written in the 1st Temple period, if I recall my linguistics correctly no earlier than the 9th century BCE, quite possibly more recently, it becomes obvious that they could not have been written as historical accounts, but rather theological. As such, this question becomes looking for an answer that the text never intended to give. I suspect though that whomever the author was, they would respond that Eve spoke according to her understanding of what she had been told, and then followed up with an observation about people who did not understand what the story was telling them.

Effah, Genesis 2:16-17 states "And the Lord God commanded the man, saying, Of every tree of the garden thou mayest freely eat: But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die." God told Adam and Adam probably told Eve not to eat of the tree. Satan deceived the woman by implying that God had lied. So she ate of the tree. When Adam realized what she had done, he was not strong enough to rebuke her he was a weak man. He followed her in this rebellion. They both became spiritually separated from God. They died spiritually. They were not pure and innocent anymore. They died spiritually. God did not lie. God told Adam he would die and he did. The natural death came later. Effah, do not let a rebellious woman lead you away from God told you not to do.

According to Gen. 2:16-17 ("And the Lord God commanded the man, saying, Of every tree of the garden thou mayest freely eat: But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou latest there of thou shalt surely die." ) God does not say that if Adam will touch the tree he will die. God says only that he shall not eat of it. God says these words to Adam, for Eve was not yet created. In Gen. 3:3 it is Eve that says to the snake: "of the fruit of the tree which is in the midst of the garden, God has said, ‘You shall not eat it, nor shall you touch it, lest you die", that is not exactly what God said to Adam. Now, according to the logic, there are these possibilities: 1) Adam lied to Eve, therefore Eve did not lie; 2) Adam unwilling said to Eve a different version, therefore Eve (nor Adam) did not lie; 3) Adam said to Eve the exact words of God, but Eve lied; 4) Adam said to Eve the exact words of God, but Eve unwilling said a different version; 5) There was a special revelation to Eve by God that was not accounted in the Bible. According to the pure deductive logic, the question remains unsolved. If we want to give an interpretation above the pure text and its inner logic, we can say that Eve's words "nor shall you touch it" seem to give a bad image of God, such as a strict guardian. But, of course, it remains only a personal interpretation. What is not interpretation, but a matter of fact, is that the snake, i.e. the devil, is "the father of lies".