LotR is generally published in three named volumes, but each volume is broken up into two "books" (in this context, meaning a major division of a literary work, not a set of bound pages). FotR, Book II starts with the chapter "Many Meetings" (when Frodo wakes up in Rivendell).

There are only 3 LOTR books

No, there are 6. To quote the "note on the text" at the beginning of my 1-volume edition:

The Lord of the Rings is often erroneously called a trilogy, when it is in fact a single novel, consisting of six books plus appendices, sometimes published in three volumes.

Each of the common three volumes consists of two books, which should be clearly delineated as such in any copy.