God did not lie. Within 960 years, Adam and Even both died - a "day" equivalent to scripture that says "a thousand years is but a day to the Lord, and a day as a thousand years." Psalm 90:4, 2 Peter 3:8. And Satan lied. They did die.
In the next passage you refer to, the "us" God is referring to is to the Heavenly Host who is watching the whole thing. This could include all the angels, or the other persons of the Trinity, or both - because the next phrase codifies specifically who "us" is - an "us" who "lives forever."
There were two trees in the Garden. One tree could not be eaten from. Hebrew tradition states that when God gave Adam the choice "to eat from any tree in the Garden, except the Tree of Knowledge of Good and Evil" it was actually a choice between the eating from the Tree of Life (which he did eat of course before the fall) or the Tree of Knowledge of Good and Evil.
The moment Adam sinned and ate from the wrong tree, death entered - a process that would take less than 960 years to complete. Had he eaten again from the Tree of Life, death would have halted, and Adam would not have died. But God did not want Adam to live forever, because if he did, then Adam would be just like the fallen angels that rebelled: Lucifer, who became Satan, and the angels that became demons: their ability to live forever has made their rebellious, sinful, and now imperfect condition - PERMANENT - forever. God loved man so much that he wanted to give them a second chance, but he had to withold the Tree of Life from him, until a day came when He Himself would BE the Tree of Life hanging on a cross 4000 years later, and man's sinful nature could be completely changed and reversed. - the debt of sin, death, would be paid in full. And now, man can live forever as perfect...again.