Lydia a widow in 1871 but no Bolton Deaths for John Mather of a similar age. However, 1870 Royton death is a good match (although burial has wrong age).
Not with family in 1851 but Betsy born 1874, so may have survived.
Lancashire Death indexes for the years: 1870 MATHER John 35 Royton Oldham ROY/14/51
MATHER, JOHN 35 GRO Reference: 1870 D Quarter in OLDHAM Volume 08D Page 438
Burial: 3 Nov 1870 St Paul, Royton, Lancashire, England John Mather - Age: 39 yrs Abode: Royton Buried by: Richard Hill Register: Burials 1868 - 1879 from the Bishop's Transcripts, Page 58, Entry 462 Source: LDS Film 1545722
General Notes
In 1861, John married Lydia Nightingale at Bolton, St James, Breightmet.
John and Lydia were married in a religious ceremony in September 1861 at St. James (Breightmet).4 They had a son and three daughters, named James, Elizabeth, Ann and Ellen. There are no more children.