If our salvation is secure, how can Christ blot out our name?

I believe that the book of life is a record of all who are living whether on earth or in heaven. In one place, it is called "the book of the living" (Psalm 69:25Let their habitation be desolate; and let none dwell in their tents.
See All...). Therefore, when we are conceived, we are placed in the book of life because we are in "the land of the living" (this phrase is found 15 times in the Bible - see Job 28:13Man knoweth not the price thereof; neither is it found in the land of the living.
See All...; Psalm 27:13I had fainted, unless I had believed to see the goodness of the LORD in the land of the living.
See All...). Those who are saved never have their names removed from the book of life because they never really die. They go on living forever. However, those who are lost have their names blotted from the book of life when they die. They are given over to death and are no longer in the book of life.

Even the lost owe their life to God. He "giveth to all life, and breath, and all things" (Acts 17:25Neither is worshipped with men's hands, as though he needed any thing, seeing he giveth to all life, and breath, and all things;
See All...). "For in him we live, and move, and have our being" (Acts 17:28For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring.
See All...). Therefore, the life of God is known by all men--even if it only refers to physical, and not spiritual, life. But they know something of life, for the life of God has given them life.

As long as there is life, there is hope that someone can find eternal life. They are among the living for whom Christ died. "And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world" (1John 2:2And he is the propitiation for our sins: and not for our's only, but also for the sins of the whole world.
See All...). However, when they die without Christ, they are blotted out from the book of life because there is no longer any hope for them. "And as it is appointed unto men once to die, but after this the judgment" (Hebrews 9:27And as it is appointed unto men once to die, but after this the judgment:
See All...).

Those who overcome, as in Revelation 3:5He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels.
See All..., have overcome by their faith in Jesus Christ. 1 John 5:4-5 [4] For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith. [5] Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
See All... states, "For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith. Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?" Since they have overcome, they do not really die when they die. That is why the Bible refers to believers as sleeping. Their body sleeps, but their soul and spirit are alive with God.

However, the lost go directly to an eternal death. They exist, but they exist in an everlasting death. They have been blotted out from the book of life.

It also may be that the Lamb's book of life is distinct from the book of life described above.

Revelation 13:8And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world.
See All... And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world.

Revelation 21:27And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.
See All... And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.

The Lamb's book of life seems to have those written in it who have been redeemed by the blood of the Lamb of God--Jesus Christ. There is no mention of being blotted out of this book. Therefore, the way to avoid being blotted from the book of life is to get your name written in the Lamb's book of life.

One final thought: if all men are in the book of life, then there is hope for them as long as they live. We need to strive to make sure that more of them continue to live--even when they have left the land of the living. We need to take to them "all the words of this life" (Acts 5:20Go, stand and speak in the temple to the people all the words of this life.
See All...) about how to trust in "the Prince of life" (Acts 3:15And killed the Prince of life, whom God hath raised from the dead; whereof we are witnesses.
See All...) so that their names will not be blotted from the book of life.