What is the Book of Life? It’s not a physical book. God does not need the assistance of a created thing for keeping track of our works nor for knowing who actually belongs to Him. As St Thomas writes:
A thing is said metaphorically to be written upon the mind of anyone when it is firmly held in the memory, according to Prov. (3:3): Forget not My Law, and let thy heart keep My commandments, and further on, Write them in the tables of thy heart. For things are written down in material books to help the memory. Whence, the knowledge of God, by which He firmly remembers that He has predestined some to eternal life, is called the book of life.
God knows His people. Let us strive diligently to be faithful to the One who has called us.