The Book of Lamentations is a collective work of poetic laments for the destruction of Jerusalem.  Traditionally, authorship is ascribed to the prophet Jeremiah, who also authored the Book of Jeremiah but this was due to a reference in 2 Chronicles to the prophet composing a lament on the death of King Josiah.  Since there is no reference to Josiah in the book, many think there’s no reason to connect Jeremiah to it. Also, there are gender and first person changes that suggest the book may be a collection of laments from multiple authors.  The book was probably written around 590 BC.