Just to add to the general chorus:
--Booked a TATL itinerary in mid-winter for travel in spring.
--LH cancelled the outbound U.S. to Europe legs in mid-March; I held off requesting a refund in the hope that TATL traffic would sort itself out by July (it was a cheap fare, thus to defer the decision did not unbearably impact my budget).
--Given forum members' reports of problems with refunds, in April and again in May I called Peterborough for re-confirmation that I still had the choice whether to rebook or ask for a refund; both times the agent on the line re-confirmed that it would be possible to do either.
--Now with the continuing disruption in normal TATL traffic for the foreseeable future, I decided today, July 1, to request a refund.
--The agent -- in CPT by the sound of it -- initially tried to push some codswallop that, since I had agreed to put the PNR into dormant status, it would only be possible to rebook, not ask for a refund.
--After some back-and-forth she reluctantly agreed to get her supervisor's approval to put through a refund ("two to six weeks"). She and her supervisor refused to put in writing anything other than the standard one-line e-mail that "Unfortunately we had to cancel your booking on 01 July 2020" but apparently did annotate the booking file to confirm approval for a full refund.
So for now no tale of woe.
My travel pattern locks me into using LH Group. Status is a useful buffer in the event of irrops. Moreover, there are members of this forum who will hasten to proclaim that they have never had less than an immaculate experience with LH. Therefore, who needs yet another observation about LH senior management's graceless, transactional approach to customer service (and to their cabin crews as well) since CLIMB and SCORE? A pity though...