loop through all the terms of a book_category taxonomy
construct a meta query array wherein a date_live date field added using ACF is checked for its value between the first and last days of the current month
for each taxonomy term create a WP_Query object having all the entries of the book post type that belong to that term AND meeting the above meta query requirement i.e., the month of date-type custom field's value matching the current month.
output the taxonomy term headings and book titles in the loop
to have entries of a CPT grouped by a taxonomy where the date-type custom field's value falls in the current month.