No. They did not die that day. And God didn't say that they would die that day. He said, On the day that you eat of the tree, "dying you shall die." In other words, the day that they died, they would be lost forever. If someone is dead in their transgressions, the day they die they will be lost forever. If someone is alive in Christ, then the day they die is not the end of their story.
No soul is "lost forever" as you put it until cast in the LOF and removed from the Lamb's book of life. Adam and Eve are not lost until they stand at the GWT Judgment event mentioned in Revelation 20. That is if you still claim the are "dying you shall die". The first death is physical. The last death is cast into the LOF.
They did physically die. Their souls were taken out of God's permanent incorruptible physical body and placed in a temporal corruptible physical body of death, thus the term mortal. Adam's flesh is the flesh of death. All physical death is, at the end of their life, is God removing them from society, and they can no longer serve God for eternal reward, be it good or bad. Those who stand at that GWT will also be judged for their works:
"And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works."
So John starts out with books open, and then inserts a seperate book, the Lamb's book of life. God's redemption is being named in the book of life, but remaining in that book is still the decision each individual makes. God still does not redeem a soul because of their works. They were redeemed by the Atonement Covenant, the blood of Jesus on the Cross. The Second Death is awarded to all who choose at that point to be removed. The works judgment is related to their eternal punishment or reward, not exactly their destination. Remember Daniel saw some judged on that day who are proclaimed righteous.
The issue is that this is not the last judgment for the entire human race since the 6th day, as some declare. A thousand years earlier there was another judgment. The Cross was a judgment that allowed those OT redeemed to be set free from death and they were presented to God in Paradise. They left the confines of Abraham's bosom as souls and were given permanent incorruptible physical bodies.
The first resurrection is physical and the soul puts on a permanent incorruptible physical body. That body came out of the grave as Jesus declared, the same as Lazarus had that body when he was called out by Jesus from his grave. But that hour has been ongoing since 30AD. A redeemed soul is called out of their grave, this mortal body of death, at the moment the soul leaves earth and enters Paradise into a new permanent incorruptible physical body. Those in Christ were already rising first in Paul's day. For a person who follows Christ, born from above by submission to the Holy Spirit, the second birth, this body from Adam is our only grave.
We do not taste death having the second birth. The day of redemption is when the soul leaves death and enters eternal life. That has been a different point in time for each individual. That is not some future general resurrection. Those in Christ with the second birth can never taste death, so once physically dead, they have left death entirely, and are no longer considered "the dead". They are not physically dead nor spiritually dead, but are blameless, soul, body, and spirit. There is nothing they can do to change that fact once they have left Adam's dead corruptible flesh behind them. All in Paradise have experienced the first resurrection.
"Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power."
They have been serving God day and night in that heavenly temple since the Cross and Resurrection. That is not a future promise. That has been an ongoing reality since the first century. When the fulness of the Gentiles is complete, there will be an innumerable multitude from every generation since the Cross. But they are not waiting as souls in stasis somewhere. They have been translated out of death into life, and have that physical body those created on the 6th day have. It was only Adam and Eve's descendants who were mortals in a physical body of death. Those souls from Noah's day and spirits to whom Jesus preached to after dying on the Cross, were not all Adam's offspring. They were destroyed in the Flood, but waited in sheol until the Cross. They were not alive after the Flood, nor part of faith, nor the Law. But they were preached to in their punishment, and given the gospel in sheol. They had no excuse of not being allowed repentance, but they had to wait until the Cross to understand, and experience redemption. They rejected the safety of the ark to live on in sin, and they certainly did not repent, because they were all destroyed.
Some may argue that Noah preached redemption. Had any one or many too great to fit in the ark repented, perhaps the Flood would have not happened like in Nineveh, but we will never know, because no one joined those 8 and by faith entered the ark. No one of that wicked group were spared to live along side Noah and his family. The same is true about the Millennial Kingdom. Only the redeemed will live on earth. No one in Adam's dead corruptible flesh will be allowed to corrupt the Millennium.
Does no one get the reference to Peter's comparison of the Flood of water to the Baptism of fire of the Second Coming of Jesus as King? It will not take a thousand years to weed out this death. The winepress of God's wrath is the end of the road for Adam's punishment of sin and death. Only the redeemed come out on the other side of this Baptism of Fire. Just like only Noah and 7 others came out of the ark after the Flood. No other humans were spared hiding out somewhere. The redeemed sheep and wheat of the final harvest are who restore life on earth and subdue and multiply to fill the earth restored after that judgment of fire. 2 Peter 3:6-7
"Whereby the world that then was, being overflowed with water, perished: But the heavens and the earth, which are now, by the same word are kept in store, reserved unto fire against the day of judgment and perdition of ungodly men."
There is only one more time of judgment of earth, and prior to the Millennium. No judgment will be necessary after the Millennium. Creation will be whole not corrupt at the end. The only thing consumed by fire at the end are those humans who listen to Satan. Peter states the Day of the Lord
comes, not
ends in fire.
"But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up."
The destruction and cleansing happens at the start of the Millennium, not after this Day of the Lord. Nor will the entire day be filled with destruction and cleansing. The Trumpets and Thunders happen before the 7th Trumpet declares time to be fulfilled. Jesus is on the earth with this Baptism of Fire. The one John the Baptist declared when he was talking about Jesus.
"I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:"
