Which part didn't you understood? Death in Christianity is a bit different understood than in secular world. Death from God's point of view is to be separated from God and all what God wants for you. So God didn't lie, man was cast out of Eden so actually he died - was seperated from God in the very day of wrongdoing.
That is exactly the bit I don't understand. That death doesn't really mean death. It means God being mad with you. What he said was "You will positively die", but what he meant was apparently "I will throw you out of the garden, inflict random and arbitrary hardships on you while still expecting you to worship me".
What then was the tree of life? Had they managed to thwart God's plan and eat from it, would they have been welcomed back into the sight of God, or would they have lived forever as a straightforward reading of the story seems to imply?
Knowing good and evil by experience actually means to become evil. That's what happened and evil can't be in presence of God. You don't have to know evil by experience to survive in God's presence, so it was not necessary actually for man.
So what did YHWH mean when he said "The man has become like one of us, knowing good and evil"? That he had become evil like YHWH and his companions?
But what snake sayed is that actually God is lying and hiding something from man. That God does not want for man something good, and man believed snake rather then God even when man had experience of God's grace in Eden and didn't have any base to believe in snake. Lying in it's pure form - to change good and evil!
No, what happened is what the snake said would happen, they became like God knowing good from evil. Because YHWH's deception was discovered, he decided to torture and kill them.
This is what happenning today globally - good becomes evil and evil becomes good.
Clearly, if you believe that YHWH, the murderous liar in the story, was good, and the serpent, who revealed the deception, was evil.
And by separation from God comes corruption which end's in ordinary fleshy death.
Separation from God in the Bible always seems to be beneficial. It's only those who get involved with the bullying YHWH that seem to have problems.