Revelation 3:5 (DRB):
5He that shall overcome shall thus be clothed in white garments: and I will not blot out his name out of the book of life. And I will confess his name before my Father and before his angels.
From Revelation 3:5, Could a written name in the book of Life be blot out? Blot out=erase.
I mean, is Free will present?, Even after being written in the book of Life, i.e: choice between good and evil is present, even after being written in the book of Life.
Thus, a man can get in, or get out, or re-enter in the book of Life.