While what you experienced was absolutely horrible, it was exacerbated by the fact that on Sunday around 6 PM, a trade union announced that all Lufthansa ground staff will go on strike from Tuesday early morning until Wednesday morning. So, while you were trying to sort out your issue, there were literally thousands of other passengers scrambling to get their flights rerouted (I know, I was one of them). That would likely explain why you got only clueless, unempowered agents, who were frazzled and had no authority to do anything, or no supervisors available to advise them (as they were likely held up on other escalations).

Not justifying or excusing Lufthansa at the slightest, just shedding some more light at the utter mess you experienced.