Funnily enough I just had a similar interaction with Lufthansa but the result was much different, within half an hour of filling in the relevant form I got the reply with the proper compensation amount and within 2 days entering my bank details the transfer was complete. Good to have the view on different airlines
Lufthansa moved my girlfriend's flight by an entire day and then when calling in, the worker even admitted it saying she could see she was never informed. She found this out upon arrival to the airport. They never did anything for her. After she kept the tickets leaving a day later, on one of her legs she missed a connection and had to spend the night and they refused to do anything for her. Not pay the hotel not pay a late fee, nothing. In fact, they didn't even get on the phone with here at the airport.
Lufthansa has changed flights on me and never done anything for it and basically just said "cancel it and take back the 15% which is taxes which we'll return to you". At the time I didn't have the bandwidth to do anything else. They never even paid and it's too much energy to even get anyone to acknowledge this.
Fact is Lufthansa also is a shit organization. The correct thing is to either (1) with minimal effort send official complaints to government agencies with documentation, (2) to hire one of those companies to just do it for you, or (3) go zen and just stop caring that companies are breaking their contracts and ignoring their legal obligations.
Sure sometimes it works, but no Lufthansa isn't one of the good airlines. They're just as corrupt as the rest.