Hi Kris,
Ringkøbing is both a parish and an amt(similiar to a state in the US). The church records of Denmark are the official records so the death of William H. Lee would be listed. I looked through the 1901 death records for Ringkøbing parish and his death is not listed there. There are probably 100 or more parishes in Ringkøbing amt.
Sincerely,
Paul
North Carolina, USA