And if anyone's NAME was not found WRITTEN in the BOOK OF LIFE,
Let's think a little bit about a person's NAME. We are given a NAME at birth by our parents, usually. That name is associated with our physical appearance. But, spiritually, we are named at conception. Our birth name may well be a duplicate of someone else's name. But the names in BOOK OF LIFE must be unique for the judgment to be correctly meted out. Only in recent years has science shown the uniqueness of DNA (actually DNA, genotype and phenotype1). Thus, I suspect, we are known to God by our genetic structures. There are some interesting implications to this concept.
If life begins at conception (or very shortly thereafter), then a life taken anytime prior to the "natural" physical death of the being is considered murder. Murderers are listed in Revelation 21:8 as those who will take part in the LAKE OF FIRE. The spiritual part of each NAME then also begins at conception Luke 1:26-31-35-38 and Genesis 2:4-7-14). It will be interesting when we, believers who are alive physically, are united with these spiritual entities who are in heaven either through abortion, miscarriage, or some other death prior to the 'age of accountability', whether we will even recognize them as such. It makes us wonder what the real spiritual part of each of us individually truly is.
If the spiritual entity has reached the 'age of accountability', then it is by their individual choice to NOT believe on Jesus Christ that will force Jesus to remove their NAME (Revelation 3:5) from the BOOK OF LIFE. Knowing that the LAKE OF FIRE is not a fun place to be (for an eternity no less), a person MUST consider choosing to accept Jesus Christ as their Lord and Savior as the better alternative.
he was THROWN into the LAKE OF FIRE.
This is not an option. All options these unbelievers had are long gone. The use of 'THROWN' indicates this is a permanent removal from earth and permanent residence in the LAKE OF FIRE. You may have heard people flippantly remark, "But I'll have lots of friends there" as though that will be a comfort. The LAKE OF FIRE holds no friends; it holds individuals whose NAMES are NOT in the BOOK OF LIFE along with the devil (verse 10), the antiChrist (Revelation 19:20), the False Prophet (Revelation 19:20), all evil (demons, DEATH, and HADES in previous verse).
1 Lewontin, Richard, "The Genotype/Phenotype Distinction", The Stanford Encyclopedia of Philosophy (Spring 2004 Edition), Edward N. Zalta (ed.)