Luke Mather must have been born about the time his father died, in Jan 1827 as he was 13, a working coal miner in 1841. He was names Mather, not Boden (like Thomas and Charles), so may be the son of Thomas Mather (but was Boden in 1851).
In 1841, Luke Mather aged only 13 was a coal miner. There was another younger Luke, aged 10 at Middleton (son of Richard and Sarah). Both married Elizabeths at Manchester (1849 & 1851).
In 1851, Luke "Boden" (21) is with his parents Thomas and Betsy Mather and family at Pilkington.
20 May 1861, Luke Mather a Collier of Stand Lane, son of Thomas Mather a Barber married Betty Wood daughter of Edmund Wood, a painter at All Saints, Stand.
In 1881, Luke, a Farmer and Margeret (53 & 54) were at 7 Hermitage, North Bury with son Joseph (15).