The April to June 1858 birth index Joseph Simpson, Penrith, Cumberland, volume 10b page 365.

In the 1861 census living at Parkhead, Kirkoswald, Cumberland. Registration District Penrith, sub registration district Kirkoswald.
Head, Richard Simpson, age 39, farmer of 72 acres employing 1 man, born at Longmartin [Long Marton], Westmorland.
Wife, Mary, age 32, farmer’s wife, Longmartin, Westmorland.
Son John Simpson, age 7, farmer’s son, born at Longmartin.
Son Thomas William Simpson age 4, born at Kirkoswald, Cumberland.
Son Joseph Simpson age 2, born at Kirkoswald, Cumberland.
Son George Simpson, age 6 months, born at Kirkoswald, Cumberland.
Brother Edward Simpson, age 48, Carter (Ag. Labourer), born at Longmartin.
Niece Mary Swage?, age 18, dairy maid, born at Longmartin.

In the 1871 census living at Glendowling, civil parish of Bridge and Yanwath, ecclesiatical parish Carlise, town of Yanwath, Westmorland, registration district West Ward, sub registration district Lowther.
Head Richard Simpson, age 49, farmer of 73 acres, born at Long Marton, westmorland.
Wife Mary Simpson age 42, born at Long Marton.
Son John Simpson, age 17, works on the farm.
Son Thomas William Simpson, age 14, born at Kirkoswald.
Son Joseph Simpson, age 12, born at Kirkoswald.
Son George Simpson age 10, born at Kirkoswald.
Son Richard B. Simpson age 4, born at Kirkoswald.
Mother in Law Mary Bellas, widow, age 74, Landowners?, born at Bongate?, Westmoreland.
and 1 servant.

In the 1881 census High Crosby, Crosby on Eden, Cumberland
Servant Joseph Simpson, unmarried, age 22, farm servant, born Kirkowald
He is living with Sarah Armstrong, a widow and farmer and her family with other servants.

In the 1891 census living at the same address.
Head Richard Simpson age 69, farmer, born at Longmartin.
Wife Mary Simpson, age 62, born at Longmartin.
Son Joseph Simpson, single, age 31, farmers son, born at Kirkoswald.
2 servants, 1 agricultural, 1 domestic.

In the 1901 census Workington, Cumberland
47 Beely Street, Workington
Head Joseph Simpson, married, age 42, steelworker, worker, born Kirkoswald, Cumberland
Wife Margaret H. Simpson, married, age 32, born Addingham, Cumberland
Stepdaughter Clara M. Watson, aged 11, born Addingham
Son Frank Simpson, age 2, born Workington.

He must have died before 1911 as his mother lists only 1 living child in the 1911 census who would be her son Richard.

In the July to August 1902 death index Joseph Simpson, died age 44, Penrith, Cumberland, volume 10b, page 283.

Death year and location from the Lancaster Family Tree at Ancestry by lpauljlancaster

In the 1911 census Nelson Hill, Plumpton near Penrith, Cumberland
Head Thomas Longrigg, Agę 45, farmer, employer, born Hesket, Cumberland
Wife Margaret [as spelled] Longrigg, age 43, married 7 years, 3 children born alive - 2 still living, born Hunsonby, Cumberland
Daughter Elsie Simpson, age 21, single, farmers daughter dairy work, worker, born Hunsonby
Son Frank Simpson, age 12, school, born Workington
Daughter Alice Longrigg, age 6, school, born Penrith
Son Joseph Longrigg, Agę 5 months, born Plumpton
2 general servants

In the 1921 census Nelson Hill, PLumpton, Penrith, Cumberland
Head Thomas Lonrigg, age 55 years 4 months, married, born Hesket, Cumberland, farmer, employer
Son Joseph H. Longrigg, Agę 10 years 8 months, born Plumpton, whole time at school
Step-son Frank Simpson, age 22 years 9 months, single, born Workington, assisting step-father in general farm work
Wife Margaret H. Longrigg, age 53 years 2 months, married, born Hunsonby, Cumberland, home duties
Step-daughter Elsie M. Simpson, age 30 years 8 months, single, born Penrith, home duties
Daughter Alice Longrigg, age 16 years 11 months, single, born Penrith, home duties