Thanks to Jan for the following information:
Lydia was a daughter of David Kemp (1818-1870) & Mary Cooper (1816-1878) of Norfolk, England. She married James Loveday in May 1862 at Forncett St Peter Norfolk England. They emigrated with 7 of their 15 children

James & Lydia arrived in Napier, as assisted immigrants, on the Schichallion which left London 10 Feb 1874 and arrived in Napier 26 May 1874. Their 9 month old infant Daniel died aged 9 months, from bronchitis, a month into the voyage. Also on board was Lydia's mother, 49 year old Mary Kemo, Lydia's brothers Daniel, Edward, Elijah & sister Elizabeth Kemp (all single) and her brother Frederick, his wife Harriet and their 3 children, 6 year old Elijah, 4 year old Willie, 2 year old Harriet and a baby daughter born 27 March 1874. They all settled in Woodville as part of the original Woodville Farm Settlement.
The passenger list of the Schiehallion .. http://tinyurl.com/323rt7dx
Lydia's brother Edward Kemp (1857-1932) is buried in Old Gorge, Woodville

Lydia's children
1862 - 1925 George Loveday (+Doney)
1863 - 1931 Florence Loveday (+Walker)
1855 - 1947 William Loveday (+Walker)
1868 - 1931 Eliza Loveday (+Ingpen)
1869 - 1941 Sarah Loveday (+Long)
1872 - 1896 James Loveday (didn't marry)
1873 - 1874 Daniel Loveday (age 9 months)
. died at sea on the Schiehallion
1875 - 1955 Annie Lydia Loveday (+Pattison)
1876 - 1953 Grace Loveday (+Cross)
1877 - 1890 John Loveday (age 12)
. buried Old Gorge Woodville with sister Elizabeth
1879 - 1934 Mary Loveday (+Treloar)
1881 - Lilly Rebecca Loveday (+Casey)
1883 - 1947 Emily Jane Loveday (+Scott)
1884 - 1887 Elizabeth May Loveday (aged 2)
. buried Old Gorge Woodville with brother John
1890 - 1954 Ethel Maud Loveday (+Whitten)

Waikato Times, 13 Jan 1920
LOVEDAY - On January 12th, at the residence of Mr R. Casey, Matamata, Lydia, relict of the late James Loveday; aged 70 years. The funeral will leave Clarence Hall for the Hamilton West Cemetery at 2.30 p.m., on Wednesday.