The destruction of Jerusalem by the Babylonians in 587 BC is the likely setting for the book of Lamentations.
It is out of that unspeakable pain that Lamentations speaks, in poet.
This was the most traumatic event in the whole of Old Testament history, with its extreme human suffering, devastation of the ancient city, national humiliation, and the undermining of all that was thought to be theologically guaranteed like the Davidic monarchy, the city of Zion, and the temple of the God of Israel.
The destruction of Jerusalem by the Babylonians in 587 BC is the likely setting for the book of Lamentations