Consider 2 Corinthians 5:14-21 (WEB),
14) For the love of Christ constrains us; because we judge thus, that one died for all, therefore all died. 15) He died for all, that those who live should no longer live to themselves, but to him who for their sakes died and rose again. 16) Therefore we know no one after the flesh from now on. Even though we have known Christ after the flesh, yet now we know him so no more. 17) Therefore if anyone is in Christ, he is a new creation. The old things have passed away. Behold, all things have become new. 18) But all things are of God, who reconciled us to himself through Jesus Christ, and gave to us the ministry of reconciliation; 19) namely, that God was in Christ reconciling the world to himself, not reckoning to them their trespasses, and having committed to us the word of reconciliation. 20) We are therefore ambassadors on behalf of Christ, as though God were entreating by us: we beg you on behalf of Christ, be reconciled to God. 21) For him who knew no sin he made to be sin on our behalf; so that in him we might become the righteousness of God.
This passage clarifies a few things. Just because Jesus has written every human being's name in the Lamb's Book of Life does not mean everyone is saved in every dimension. Christ has died for all mankind, but not all live! God has reconciled all mankind to himself through Christ, but not all acknowledge their forgiveness in Christ. All are forgiven, but not all are saved from the prideful refusal to be happy about forgiveness, and others are simply ignorant of the good news. Most of those in the Lamb's Book, the elect, are still unbelieving, and unless they are graced with faith they will suffer punishment in Hades for their unbelief. The first born nature of rebellion still rules their heart.
We know this to be true for no one is born with faith. Each individual must be born again through the Holy Spirit and come to faith in Christ to know God. Even though the unbelieving elect are saved from the Lake of Fire, they are not saved from unbelief and punishment in Hades unless they repent. Even though their names are in the Lamb's Book of Life they will still suffer punishment in Hades for their rebellion. Furthermore, even many Christians who are saved from Hades are also not saved from sin and the consequences of sin. Even though Christians are blessed children of God and saved from Hades, we can still ruin our earthly lives with sin. Salvation has numerous dimensions including rescue from the Lake of Fire, from Hades, and from sin as I discuss in my article, SAVED 5X. Jesus warned that broad is the road to destruction and many enter through it!
Now what if someone were persuaded that his name is in the Book of Life, yet instead of serving Christ in gratitude, he simply lived like the Devil for his selfish interests? Such a person is certainly the fool mentioned in Proverbs 26:4-5. Such a person could hardly dare to call himself a Christian or a follower of Christ. Regardless of the hope of the Good News, such a person really has no hope. Such a person lives a life of fearful expectation of the coming judgment. Furthermore, Romans 10:9 makes it clear that to be truly saved one must both confess with the mouth and believe with the heart. Punishment in Hades awaits everyone without a Christian heart. The Scripture has important words of warning for such a person which I will come to shortly.
Again, the Scripture above confirms that Christ has died for all. These verses even explain that all mankind is already positionally reconciled to God "in Christ" apart from faith. Most would teach that each individual is placed "into Christ" only as he believes in him. But I understand that those predestined to salvation are never outside of God's grace because they are always positionally in Christ. However, as each individual is awakened as a new creation, he realizes his position in Christ and begins to live in Christ. The elect of God are in desperate need of the salvation of their hearts through the new birth. However, God's gracious purpose for his chosen ones was decreed before we believed, before we were born, and even before creation. See my article 'In' Doctrine for further discussion.
A related thought is that most Christian theologies suggest that justification, the legal proclamation of our right standing with God, happens per individual either immediately before or after personally trusting Christ. However, I suggest that justification was pronounced for all God's people one time at the cross. Again see my article Justified! for more details.
Unfortunately too many professing Christians imagine or have been taught that the free will choice of "faith" is the activating ingredient in our personal salvation. They imagine "faith" to be like a string that reaches from their prayer to Heaven's courtroom to hammer the gavel of their justification.
However, picture this: a venomous criminal with only the courtroom floor between himself and the lawful judge that he hates. If the police were not restraining him and the judge's bench was not so high, he would simply reach out and kill the judge. We know this to be accurate imagery because there was one time in history when the judge stepped down from his bench. We know that God's holy angels were commanded to stand by. The good judge gave himself into the hands of the criminal. Mankind universally conspired to kill the Christ! When will such a venomous criminal ever exercise his free will to repent? He does not even want to be saved. He does not want to be at peace with the judge. He hates the judge. He wants to kill the judge! He wants to be his own judge... and the judge of everyone else. But he just cannot reach the gavel of justification across the courtroom floor. The true judge will not relinquish the gavel to the criminal because he is the good judge. The criminal cannot change his heart to begin to love the judge because he hates the judge BY HIS VERY NATURE. He is not free, but locked in bondage to sin. Even if the criminal could suddenly begin to be good, it would not be enough to mend the error of his past rebellion. Even if the criminal would magically transform into Mother Teresa, he still must pay the price for his past crimes. Claims of free will decisions for Christ and "faith" that "writes our name in Heaven" simply miss the heart of grace.
The crux of the matter is that Jesus Christ imputed righteousness to our account while we still hated him and while we loved only ourselves, according to Romans 5:10. The essential point is that there will never be any positive change until God himself reaches inside the individual's life to replace his heart of stone with a heart of flesh. The good news is that Christ alone has sacrificed his body and poured his blood on the Father's righteous bench to proclaim our justification. He did this while we criminals were still spitting out venom dressed in our rags of self-righteousness. But the sound of Jesus' gavel silences Satan, the prosecuting attorney, who still drones on listing our sins for an easy indictment. All of this transpires before the courtroom audience. God's holy angels are astonished that Christ could forgive us, the very partners of Satan. They never cease to marvel over God's glorious grace toward his redeemed.
Of course most of us do not appear to be venomous criminals... at least not until our self-righteous attitudes are confronted with God's glorious grace and Christ's love for ALL mankind.
If you are an evangelist consider that the purpose of evangelism is NOT to add names to the Book of Life! How can we do that anyway? Instead, consider that the purpose of evangelism is to bring the elect of God from unbelief to belief, from spiritual death to spiritual life, from disobedience to obedience, and from certain punishment with the wicked in Hades to joyful communion with Christ... to receive Christ's finished work on their behalf.
Lastly, 2 Corinthians 5:16 also tells us that we are not to view others from a worldly point of view. The world believes that some are evil, but only those who do good meet a good end. Someone once told me that all unbelievers think that everyone will be saved in the end. Friends, I have yet to meet an unbeliever who thinks that all are saved. They typically believe there are at least enough people worse than them to fill the seats in Hell so that they will not have to go there. Thus on this point, Arminianism and Calvinism both speak from a worldly point of view.