It seems it's possible to be removed from the BOL.
Exod 32:33; The LORD said to Moses, "Whoever has sinned against Me, I will blot him out of My book.
Psa 69:28; May they be blotted out of the book of life And may they not be recorded with the righteous.
Rev 3:5; 'He who overcomes will thus be clothed in white garments; and I will not erase his name from the book of life, and I will confess his name before My Father and before His angels.
John 6:66; As a result of this many of His disciples withdrew and were not walking with Him anymore.
Php 4:3; Indeed, true companion, I ask you also to help these women who have shared my struggle in the cause of the gospel, together with Clement also and the rest of my fellow workers, whose names are in the book of life.
Some say everyone names are in the BOL (from the foundation of the earth) But some are erased at some point.
Others say it's when you get saved. Still others say it's when you pass the test of faith.
Rev 13:8; All who dwell on the earth will worship him, everyone whose name has not been written from the foundation of the world in the book of life of the Lamb who has been slain.
Rev 17:8; "The beast that you saw was, and is not, and is about to come up out of the abyss and go to destruction. And those who dwell on the earth, whose name has not been written in the book of life from the foundation of the world, will wonder when they see the beast, that he was and is not and will come.
It seems all our deeds are in the BOL. (good and bad)
Rev 20:12; And I saw the dead, the great and the small, standing before the throne, and books were opened; and another book was opened, which is the book of life; and the dead were judged from the things which were written in the books, according to their deeds.
Rev 20:13; And the sea gave up the dead which were in it, and death and Hades gave up the dead which were in them; and they were judged, every one of them according to their deeds.
Rev 20:14; Then death and Hades were thrown into the lake of fire. This is the second death, the lake of fire.
Rev 20:15; And if anyone's name was not found written in the book of life, he was thrown into the lake of fire.
Rev 21:27; and nothing unclean, and no one who practices abomination and lying, shall ever come into it, but only those whose names are written in the Lamb's book of life.
Luk 10:20; "Nevertheless do not rejoice in this, that the spirits are subject to you, but rejoice that your names are recorded in heaven."