An Etymological Dictionary of the German Language/Annotated/Lücke
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Lücke, feminine, ‘gap, chasm,’ from Middle High German lücke, lucke, Old High German lucka, from *luggja, feminine, ‘hole, gap,’ closely allied to locker (Middle High German loger, Upper German luck). The Upper German dialects contain a primary form *luggia (Swiss lugg, not lukχ), hence Old High German luccha, ‘gap,’ is abnormal. For this reason too the phonetic relation of the word to Loch is obscure.