According to an understanding of the Scriptures by many people (e.g. C.S. Lewis) everyone’s name is in the Book of Life because of what Jesus did on the Cross. But are you living in such a way that God will have to blot you out of it?
So Moses went back to the Lord and said, “Oh, what a great sin these people have committed! They have made themselves gods of gold. But now, please forgive their sin—but if not, then blot me out of the book you have written.” The Lord replied to Moses, “Whoever has sinned against me I will blot out of my book. Exodus 32:31-33
May they be blotted out of the book of life and not be listed with the righteous. Psalm 69:28
The one who is victorious will, like them, be dressed in white. I will never blot out the name of that person from the book of life, but will acknowledge that name before my Father and his angels. Rev. 3:5
Anyone whose name was not found written in the Book of Life was thrown into the Lake of Fire. Rev. 20:15.
Nothing impure will ever enter it, nor will anyone who does what is shameful or deceitful, but only those whose names are written in the Lamb’s book of life. Rev. 21:27
According to the bible, Jesus’ death on the cross and His resurrection is not a partial means of salvation for the sins of the world. Jesus is called the Lamb of God who was slain to take away the sins of the world – all its sins for all time, not just some of them:
But when this priest had offered for all time one sacrifice for sins, he sat down at the right hand of God. Hebrews 10:12
For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God. 2 Cor. 5:21
As a result, many theologians over the centuries have come to the conclusion that the default position of everyone born into the world is that they start off with a clean slate and are written into the Lamb’s book of life. This means, for example, that every innocent aborted child is in heaven.
The consequence of this way of thinking is that God has to – reluctantly – blot people out of the Book of Life when they consistently choose the devil and his ways over God and His ways. John mentions this possibility in 1 John 5:16-17.
So this understanding means everyone is saved (in the sense of not going to hell or the lake of fire when they die) but it is possible to lose that salvation by persistently sinning in destructive ways. Sadly, many, people do persist in sinning in that way, they are children of Adam after all.
By contrast, other evangelical theologians would say that no one is in the Book of Life to start with and that you have to consciously believe in Jesus – have faith – to be written into it. Since faith comes by hearing and hearing by the word of God (Romans 10 – read the whole chapter), the consequence of that way of thinking is that unless you preach the gospel to every creature they are all going to hell, innocent children included.
Taking this position explains the emphasis found in evangelical churches on simply telling as many people as possible the good news and not speaking a lot about the other things the bible says – because none of them are as important as this. People who sincerely believe this position have to say that anyone who hasn’t heard the gospel and believed in Jesus is going to hell but it is possible to avoid that fate if we can only tell people the gospel soon enough and give them a chance to believe.
It is not an easy subject.
Personally, my position is that people have to make consistent choices to walk away from God before he, reluctantly, removes their names from the Book of Life – I follow the reasoning of the first group above which includes people like C.S. Lewis. Having studied the subject for many years I think it is more consistent with Scripture.
The reason we preach the gospel then is so that people will fall in love with the One who has saved them without them having to do anything (by grace you are saved), know why they should continue to persevere in doing right and, by having a relationship with God through the Holy Spirit, receive the power to do so. Otherwise we do have a tendency – inherited from Adam – to walk away, the history of the human race as shown in the Scriptures makes this clear.