How did God lie? Adam and Eve did eventually die, did they not? Death was the result of disobedience, however, death is not final. Adam and Eve had to die and God forbid them to continue to eat of the Tree of Life because then, they would be "fixed" in a state of corruption.
By God allowing them to die, He could then give them "new" bodies and a "new" spirit.
As Jesus said in the book of Mark as a parable...
Mark 2:22 And no man putteth new wine into old bottles: else the new wine doth burst the bottles, and the wine is spilled, and the bottles will be marred: but new wine must be put into new bottles.
and in the book of Luke.....
And no man putteth new wine into old bottles; else the new wine will burst the bottles, and be spilled, and the bottles shall perish. But new wine must be put into new bottles; and both are preserved.
The "bottles" being a figurative statement referrering to the "body" and the "wine" being a figurative statement referring to the "spirit".
Then death will be destroyed....
1Corinthians 15:26 (KJV) The last enemy [that] shall be destroyed [is] death.
1Corinthians 15:54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
Revelation 2:11 He that hath an ear, let him hear what the Spirit saith unto the churches; He that overcometh shall not be hurt of the second death.
Revelation 20:6 Blessed and holy [is] he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
Revelation 20:14 And death and hell were cast into the lake of fire. This is the second death.