I think that maybe the family came from Somerset England
Found a birth for possible youngest daughter Elvie LEE who died NZ 1896 age 18 years - which would put her birth year at about 1878.
Checked FreeBMD online and found birth Qrt June 1878 Elvie LEE District: Axbridge (Somerset) Vol: 5C Page: 578 Also found a possible birth for Arthur Qrt Mar 1869 LEEArthur District: Axbridge Vol: 5c Page:622
I also noted that Arthur and Ethel had a son William Lionel Wilson LEE in 1902 died 16 Jul 1966 cremated at Purewa Cemetery and Crematorium.Taking note of the middlename WILSON thought perhaps he may have used his mother's maiden name.Checked FreeBMD online and found a possible match.
William LEE married Mary WILSON Qrt SEP 1867 District: Axbridge (Somerset) Vol: 5c Page 871