God knows the end from the beginning. In understanding the things of the Garden of Eden you must understand this principle. Before ever the earth was created, God knew that Adam and Eve would partake of the forbidden fruit and fall. This is why God called and ordained Jesus Christ from before the foundation of the world to be the Savior. God knew and expected mankind to fall. This why he placed Satan and his minions on the earth and why he planted the tree of knowledge of good and evil in the garden and gave a commandment not to partake of it. He already knew that Satan would tempt Eve through the serpent and that she would succumb to the temptation. It was all part of God's plan and this is why he called a Savior before the foundation of the earth. Eve was tempted by Satan through the mouth of the serpent with the idea of becoming like God which was true. But the lie that Satan told was that she would not die.
Genesis 3:1-6
1 Now the serpent was more subtil than any beast of the field which the Lord God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden?
2 And the woman said unto the serpent, We may eat of the fruit of the trees of the garden:
3 But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.
4 And the serpent said unto the woman, Ye shall not surely die:
5 For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.
6 And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.
If we read a little further down this chapter we understand that verse 5 above was true and that man, by going through the fall, came to be more like God.
Genesis 3:22
22 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:
So the lie that Satan told was that Eve would not die. At the time of the fall, Adam and Eve experienced a spiritual death and then later we know that Adam died when he was 930 years old (see Gen. 5:5). From the time of the fall forward, all mankind who are born in this world will die unless God has a different plan for that person.