Originally Posted by SK AAR

Interesting to read but you clearly booked with an OTA which apparently the OP didn't (well, that is the Q/issue here; if the OP in reality booked with LH despite making the flight search and the payment via Google flights) so most likely not comparable to your situation. If the OP was able access the reservation and make the refund via LH.com it supports that he/she didn't book with Google flights as an OTA but in reality booked directly with LH.