Business ProfileforLufthansa German Airlines

I purchased a roundtrip ticket on Lufthansa from ********* to ********* and back for September 5-19, 2023, at the price of $849.35. En route to *********, I flew via ******* and ******. In ****** I missed the connecting flight to ********* because I was confused by the gate/boarding process. Lufthansa rebooked me on a later flight and charged me $430.91 for this flight. I continued on to ********* without incident.My return flight from ********* was scheduled to depart on September 19, 2023. When I arrived at the airport, Lufthansa told me that my entire return flight had been cancelled due to missing the connecting flight on September 6, even though I had continued on to ********* and paid for the additional ticket/fees. This was the first time they communicated this to me. I called my mom in the U.S. and she booked a new flight home for me on September 20 for $478.00. When I got to the airport, they said the credit card transaction hadnt gone through and charged me $730.24 for the return flight home. My mom looked up the credit card charge and had plenty of balance on her account, so apparently the issue had been on Lufthansas end. The $478.00 was not charged to her card. I filed a complaint with Lufthansa (FB ID ********* on October 9 requesting a refund of $252.24, the difference between $730.24 and $478.00. Ideally the entire return trip of $730.24 would be refunded, as it was cancelled by the airline with no cause. Lufthansa sent an automatic message acknowledging receipt of the complaint but never followed up. When I called them, they said I had to do everything online. When I then tried to follow up, on October 24, they sent another automatic message acknowledging receipt and saying there may be a delay due to a high level of incoming inquiries. I have not heard anything more from them.I would like my refund to be a cash refund, not a flight credit, as I no longer wish to do business with Lufthansa.