The introduction to Lamentations in the CEB Study Bible (p. 1301 OT) notes that:
Each poem has a different different tone and character. The poetry is difficult, containing many rare words and odd grammar, and the arrangement of verses doesn't always seem to make sense.
The occasion for these poems is the fall of Jerusalem and the destruction of the temple in 586 BCE. The New Oxford Annotated Bible (p. 1167 Hebrew Bible) says:
The poems of Lamentations may be dated to the sixth century, probably between 586 and 520 BCE, when the Temple was rebuilt.
The prophet Jeremiah has traditionally been identified as the author of Lamentations. Critical scholarship finds good reason to doubt that ascription. (Critical scholarship finds good reason to doubt most everything). As the introduction to Lamentations in the Augsburg Fortress Lutheran Study Bible puts it:
The writer of the poems was long believed to be the prophet Jeremiah, probably because 2 Chronicles 35:25 mentions that his laments were recorded. Second Chronicles, however, reports that Jeremiah mourned the death of King Josiah (609 b. c. e), not the fall of Jerusalem. In the end, the author of Lamentations remains unknown.
It is, of course, also possible that the poems of Lamentations had more than one author.
The book of Lamentations expresses almost unrelieved grief, horror, sorrow, and anger at YHWH who is blamed for Jerusalem's destruction. It is an ancient primal scream. The contrast to the Song of Songs couldn't be stronger. The Hebrew Bible expresses a wide range of human emotion and experience.
Several voices speak in the book of Lamentations. It is not always easy to identify who is speaking. One voice is notably absent. YHWH is silent.
A few notes from Cheryl A. Kirk-Duggan's introduction to Lamentations in The People's Companion to the Bible (pp, 158-9):
Daughter Zion, represented as a woman, princess, widow, lover, daughter, and/or mother, personifies Jerusalem, YHWH's punished spouse....
Emilie Townes, a womanist social ethicist, reminds us that lament precedes healing. Lament asks for deliverence....Naming the pain makes it bearable.
Finally, the Harper Collins Study Bible introduction says,
The book of Lamentations is a work of art produced in response to a historical tragedy.