I got a response within two days, but I suspect that is due either to the fact that I was flying business class or because I have Senator (Gold) status with Lufthansa. I expect this put me into a completely different queue that another team works on.

I have a completely unrelated expense reimbursement ongoing with Eurowings (also part of the Lufthansa Group). There I am not getting any prioritized treatment and I am also feeling like I have no possibility to affect the processing, as in your current situation. It will come....eventually.