Names are not being added to the Lamb's Book of Life.
This may sound strange since the common belief is that our names are added to the Book of Life when we become saved, but scripture does not say that at all, in fact, scripture only ever indicates that names are being removed, 'blotted out'.
It appears that all of humanity was written down in the Lamb's Book of Life before the foundation of the earth, but those who ultimately reject the Living God and die in their sin are 'blotted out' of the book. Removed completely, leaving no trace that their name had ever been written there. At the Great White Throne Judgement, the Lamb's Book of Life will be the ultimate reference for who is alive in Christ, and a complete manifest of those who have a part in New Jerusalem.
Consider what scripture has to say concerning the Lamb's Book of Life:
There are 17 verses, found in 8 different books of the Bible, that pertain to the Lamb's Book of Life.
There are 8 verses, found in 8 different books of the Bible, that contain the word blot and pertain to the Lamb's Book of Life.
*Contains the word blot
*32:32 Yet now, if thou wilt forgive their sin--; and if not, blot me, I pray thee, out of thy book which thou hast written.
*32:33 And the LORD said unto Moses, Whosoever hath sinned against me, him will I blot out of my book.
*9:14 Let me alone, that I may destroy them, and blot out their name from under heaven: and I will make of thee a nation mightier and greater than they.
*25:19 Therefore it shall be, when the LORD thy God hath given thee rest from all thine enemies round about, in the land which the LORD thy God giveth thee for an inheritance to possess it, that thou shalt blot out the remembrance of Amalek from under heaven; thou shalt not forget it.
*29:20 The LORD will not spare him, but then the anger of the LORD and his jealousy shall smoke against that man, and all the curses that are written in this book shall lie upon him, and the LORD shall blot out his name from under heaven.
*14:27 And the LORD said not that he would blot out the name of Israel from under heaven: but he saved them by the hand of Jeroboam the son of Joash.
69:28 Let them be blotted out of the book of the living, and not be written with the righteous.
12:1 And at that time shall Michael stand up, the great prince which standeth for the children of thy people: and there shall be a time of trouble, such as never was since there was a nation even to that same time: and at that time thy people shall be delivered, every one that shall be found written in the book.
4:3 And I intreat thee also, true yokefellow, help those women which laboured with me in the gospel, with Clement also, and with other my fellowlabourers, whose names are in the book of life.
*2:14 Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
*3:5 He 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.
13:8 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.
17:8 The beast that thou sawest was, and is not; and shall ascend out of the bottomless pit, and go into perdition: and they that dwell on the earth shall wonder, whose names were not written in the book of life from the foundation of the world, when they behold the beast that was, and is not, and yet is.
20:12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
20:15 And whosoever was not found written in the book of life was cast into the lake of fire.
21:27 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.
22:19 And if any man shall take away from the words of the book of this prophecy, God shall take away his part out of the book of life, and out of the holy city, and from the things which are written in this book.