“Officials were hung up by their hands.” The commentators and versions disagree about what this phrase means. The Hebrew “by their hand” (the Hebrew is singular but can often be put for what we would understand as plural, “hands”) can be literal, that the officials were hung up by their hands as torture and to disgrace them (cp. CJB; HCSB; ESV; NIV), or it can be the simple idiom “by them,” meaning the official were hung by their oppressors, the Babylonians (cp. NAB; Rotherham).
The context favors that the officials were indeed hung up by their hands as torture and to disgrace them. The women were raped (Lam. 5:11), the elders were abused (Lam. 5:12), the young men were shamed by having to do women’s work (Lam. 5:13). It is not out of context that the officials, who would have given the orders to fight the Babylonians instead of just surrendering, would be tortured. Torturing captives was common in the ancient world, and the Bible mentions several cases of it, including the ones here in Lamentations 5:12. Women were commonly abused. They were raped, led around on ropes by hooks that went through their lips or tongues (Amos 4:2-3), and sometimes even their pubic hair was shaved to embarrass them (see commentary on Isa. 7:20).
“the faces of elders were not honored.” This is the figure of speech tapeinosis; stating something in a lesser way to magnify it. The elders were not just “not honored,” they were dishonored and treated with great disrespect.