Lufthansa cancels flights and then refuses to refund customers

My partner was due to fly home to the US on 5 July. On 27 June, Lufthansa unilaterally cancelled the flight without notice or explanation. When my partner inquired about his refund, he was told it was in the works. He’s called 3 times - every time he’s told it’s in the works. More than a month later, still no refund, and no recourse to find out what’s going on beyond the customer service desk - who always say it’s in the works. I have now re-captured the refund request from their site, but given the lack of service to date, I’m not holding out much hope of a response. There literally isn’t even an email address I can use to request an update. Disgusting and unacceptable.