The simplest and least-stressful way to deal with this is to make your request for a refund to LH and then wait 7 days. If the refund has been initiated, all the better. If not, on the 8th day you should initiate a chargeback with your credit card issuer (bank) and, in the case of tickets to or from the US, a DOT complaint as well.

With both, you should supply a copy of your e-ticket receipt, the notice of cancellation (possible screen shot showing absence of flight), your request for a refund, and any acknowledgement from LH (or a note that no acknowledgement has been received).

There is nothing extreme or hard (for you) about chargebacks and it is unlikely that LH will push back unless you have erroneously claimed a refund. DOT does not enforce individual matters, but it does evaluate whether the matter is within its jurisdiction and then send the complaint to LH requiring a response to the consumer with a copy to DOT. Given that DOT rules require a refund be initiated within 7 days, there really is not much for LH to do other than to respond that it has done so. Unless, of course, you have made an error.

By supplying the documents listed above, you make fairly short work of this for your bank as well.