Hate the sin, not the sinner, right? But when it comes to punishing the sin, you've got to bring down the hammer on the sinner pretty hard. The Poet tells us that Judah didn't obey God, so he was forced to destroy them. The interesting part is the Poet never really goes into detail about their disobedience. What did these guys do that was so awful they deserved to be exiled and watch their children starve to death? There's mention of iniquity, transgression, and disobedience, but few specifics.
One interpretation is that the author of Lamentations was deliberately vague so that the readers can fill in their own sins and think about them (source). If there were a list of sins, a reader might think, "Oh, bringing a blemished goat to the Temple? I never did that, so I'm safe."
Questions About Sin
Is there something satisfying about placing blame after a tragedy? Is it easier to blame the people for their troubles than to accept that sometimes bad things happen to good people?
Why were the prophets singled out?
What do you imagine might be the worst sins the Judeans could have committed?