Are the names of all people originally written in the Book of Life? The Bible speaks about the "Book of Life".  It seems that those whose names are written in it will have life and spend eternity in heaven whereas those whose names are not written in it will be cast into the lake of fire.


  "And I saw a great white throne, and him that sat on it, from whose
  face the earth and the heaven fled away; and there was found no place
  for them. 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. And the sea gave
  up the dead which were in it; and death and hell delivered up the dead
  which were in them: and they were judged every man according to their
  works. And death and hell were cast into the lake of fire. This is the
  second death. And whosoever was not found written in the book of
  life was cast into the lake of fire".


However, the Bible also talks about not blotting people's names out of the book of life.


  The one who conquers will be clothed thus in white garments, and I
  will never blot his name out of the book of life. I will confess his
  name before my Father and before his angels.  Revelation 3:5


So, are the names of all people originally in the Book of Life?  And then are the names of those who reject Christ blotted out of it later?  If so, what are the implications of this?

The Bible also speaks of those whose names have not been written before the foundation of the world in the book of life.


  Also it was allowed to make war on the saints and to conquer them.
  And authority was given it over every tribe and people and language
  and nation, 8and all who dwell on earth will worship it, everyone
  whose name has not been written before the foundation of the world in
  the book of life of the Lamb who was slain.  Revelation 13:7-8


So, which is it?
As with many issues I start with the Summa Theologica (Summary of Theology), by Thomas Aquinas.  Here is one section of use:  http://www.newadvent.org/summa/1024.htm#article3.

Here is an interesting quote:


  "Let them be blotted out from the book of the living" (Psalm 68:29).


So, yes, people can be blotted out of the Book of Life.

We may think we know who should be in that book, as we feel that person is achieved a particular level of holiness, but, God knows all, so there is information He will have that we don't.  So, we may feel someone is definitely going to Heaven, but later they do something that casts doubt on that, so we say they may have been removed from the Book, when they may never have been in there in the first place.

This also leads to the idea of predestination, that Aquinas covers in two parts that help here, but that goes beyond the answer to this question, so I will just give references.
This one deals with whether the Book of Life is predestination
http://www.newadvent.org/summa/1024.htm#article1

And whether those predestined for Heaven are chosen by God.
http://www.newadvent.org/summa/1023.htm#article4