I believe it is a post-V2 innovation, modeled after the books of remembrance commonly found in mainline Protestant churches. By giving it the name Book of Life, it resonated with the postconciliar changes to the funeral rites (from Requiem to Mass of Christian Burial or Mass of the Resurrection, black to white vestments and pall,no Dies Irae, less penitential emphasis, etc.), and thus seemed reasonable from a Catholic perspective. It matched what was seen in many Protestant churches, so it fit the ecumenical bill, as well as catering to the secular world’s desire to be sentimental and pleasant, and not grieving or–worse, yet–talking about Purgatory, sin, judgment, etc. Don’t misquote me–it does not openly deny any Church teaching, and if the purpose of such a book is to promote Masses and devotions being said for the dead, it is a fine practice. But as has been pointed out, the name is fuzzy, and suggests that incomplete understanding of death that non-Catholics, and increasingly, even Catholic today, have embraced. Book of the Departed would be a perfectly appropriate title and an accurate translation of Liber Defunctorum, and if used in a way that promoted a fully Catholic understanding of the last things, would be fine.