Is pile of books are lying on the correct English?

"Pile of books" is grammatically correct, but it needs a verb to make a complete sentence. Here are some examples:

* A pile of books is lying on the table.

* The pile of books are stacked neatly on the shelf.

* There is a pile of books in the corner of the room.

The verb you use will depend on what you want to say about the pile of books.