The Book Of Life, sometimes called the Lamb's Book Of Life is listing of the names of every person throughout history who has Received Christ Jesus as Lord and Saviour.
I heard Joseph Prince say that this book contains the names of every person who has ever lived. But, that those who die having rejected the Blood of Christ have their names stricken from it.
It makes sense that in the Sacrifice of Jesus Christ all Sins for all People for all Time were Forgiven, resulting in the population of the Book Of Life with every person's name.
Since we are Saved by Grace Through Faith in Christ Jesus, the permanence of our names in the Book Of Life is dependent on us being Born Again of the Holy Spirit.
Those who are never Born Again will have their names blotted out of the Book Of Life.
Whether their name has never appeared in the Book Of Life or is blotted out of the Book Of Life, the result is the same:
And whoever was not found written in the book of life was cast into the lake of fire. -