Objection 1. It seems that the book of life does not only regard the life of glory of the predestined. For the book of life is the knowledge of life. But God, through His own life, knows all other life. Therefore the book of life is so called in regard to divine life; and not only in regard to the life of the predestined.
Objection 2. Further, as the life of glory comes from God, so also does the life of nature. Therefore, if the knowledge of the life of glory is called the book of life; so also should the knowledge of the life of nature be so called.
Objection 3. Further, some are chosen to the life of grace who are not chosen to the life of glory; as it is clear from what is said: "Have not I chosen you twelve, and one of you is a devil?" (John 6:71). But the book of life is the inscription of the divine election, as stated above (Article 1). Therefore it applies also to the life of grace.
On the contrary, The book of life is the knowledge of predestination, as stated above (Article 1). But predestination does not regard the life of grace, except so far as it is directed to glory; for those are not predestined who have grace and yet fail to obtain glory. The book of life altogether is only so called in regard to the life of glory.
I answer that, The book of life, as stated above (Article 1), implies a conscription or a knowledge of those chosen to life. Now a man is chosen for something which does not belong to him by nature; and again that to which a man is chosen has the aspect of an end. For a soldier is not chosen or inscribed merely to put on armor, but to fight; since this is the proper duty to which military service is directed. But the life of glory is an end exceeding human nature, as said above (Question 23, Article 1). Wherefore, strictly speaking, the book of life regards the life of glory.
Reply to Objection 1. The divine life, even considered as a life of glory, is natural to God; whence in His regard there is no election, and in consequence no book of life: for we do not say that anyone is chosen to possess the power of sense, or any of those things that are consequent on nature.
From this we gather the Reply to the Second Objection. For there is no election, nor a book of life, as regards the life of nature.
Reply to Objection 3. The life of grace has the aspect, not of an end, but of something directed towards an end. Hence nobody is said to be chosen to the life of grace, except so far as the life of grace is directed to glory. For this reason those who, possessing grace, fail to obtain glory, are not said to be chosen simply, but relatively. Likewise they are not said to be written in the book of life simply, but relatively; that is to say, that it is in the ordination and knowledge of God that they are to have some relation to eternal life, according to their participation in grace.
Source: Summa Theologica (New Advent)