Lamentations: What Kind of Grief?

I was recently listening to a podcast on teaching Lamentations where the point was being made that the book teaches about grieving generally. While there is much grief in Lamentations, is it really about grieving in the general sense? Aren't the poetic expressions about the devastating consequences of sin against God (historically of the devastation of Jerusalem in 586 BC by the Babylonians). While the podcast mentioned sin and judgment it was almost an aside. Lamentations is not really  designed primarily as a book of comfort for those who have experienced tragic and unimaginable losses but a warning that rejecting God has tragic and unimaginable consequences. Sin and judgment frame the grief so powerfully expressed in the text.We should preach and teach it accordingly.