I have been following the trail of a Sarah Lister and think she may be your Sarah.
There are births and baptisms for more children of Joseph and Sarah, Edwin 1842 and Elizabeth 1849 and baptisms 1849 and 1850, father a clothier as on Williams baptism 1840.
This is Sarah after the 1850 baptism in Batley.
1851 Dewsbury
Joseph Sowden head widower shop keeper 1787 Halifax, Yorkshire
Sarah Lister --- married housekeeper 1818 Gildersome, Yorkshire
Elizabeth Lister daughter 1850 Morley, Yorkshire
2322/10/13
1861 Dewsbury
same people as above plus
Emma Lister daughter 1852 Bruntcliffe (which is where they are living)
Sarah now listed as servant and widow
3397/8/10
Births in Dewsbury for Elizabeth Lister 1849 mmn Holdroyd and Emma Lister 1852 no mmn, also Edwin Lister 1842 mmn Oldred
1871 Dewsbury
Sarah Lister annuitant
Thomas Smith son in law
Elizabeth Smith daughter 1849
William Ed Smith grandson 1869
4577/9/11
Marriage of Thomas Smith and Elizabeth Lister has her father filled in as Joseph Smith and crossed through and one of the witnesses was Edwin Lister.
1851-1871 Edwin is nephew of Sarah Nicholson 1791 Heckmondwike and Edwin is an Executor for the will of Joseph Sowden in 1867. He is listed as great nephew.
Emma Lister marriage to James Hardesty has father as Joseph Lister shopkeeper and witnesses Thomas Smith and Charles Akeroyd. A Luke Akeroyd was an executor in 1867 with Edwin Lister.
Marriage of Edwin to Sarah Ann Jowett has father as Joseph Lister clothier with witnesses James Marshall and Emma Chew.
This may be the connection to the Akeroyd family.
Gildersome baptisms include
1814 Harriot Holroyd
1817 Sarah Holroyd
1821 Samuel Holroyd
Zechariah and Elizabeth
1835 Birstall Luke Akeroyd married Harriet Holdroyd and 1843/46 sons Luke and Charles could be the ones mentioned.