This dispute won't go away. Still open to advice on next steps.

Recent developments:
1. I opened a dispute with Amex. They immediately credited me the airfares and closed the dispute, pending LH's opportunity to provide feedback.

2. LH finally responded to my original inquiry. Their response indicated to me that they didn't read the original complaint or didn't understand it. They sent me a generic form letter filled with many paragraphs.

3. Amex sent me a note saying they are rebilling my account based on feedback provided by LH. LH's feedback was that I had rebooked the tickets and acknowledged online that the rebooked tickets were non-refundable.

4. I did not at any point rebook the tickets. The 'evidence' that LH provided that I had rebooked the tickets was a series of screen shots for a one-way ticket that someone else had booked for June 2023 in a different currency, from a different country, with a different O/D pair entirely, in a different class of service, for a different year with a flight that departed 1 year before my, etc.

5. I reopened the dispute through Amex - but I am starting to lose confidence in the various processes.