There's a small fly in the ointment with that theory. Richard and Elizabeth Whalley have daughter Mary Ann with them in 1851. I wouldn't normally worry too much about that - people get enumerated more than once sometimes. However on both 1851 and 1861 their Mary Ann is said to be born in Steeton, nt Bingley.
Plus, there is another Mary Whalley b Bingley on 1861, once again living with an uncle in Bingley. This time it's Jonas Whalley, aged 22 33, with second niece Eliza b c1851
I also couldn't work out her connection to the Lancasters to make her William's niece. The Lancaster children have mmn Ellis or Ellice, so his wife isn't a sibling of Richard Whalley or Elizabeth King.
So I followed Jonas back to 1851
Joseph Ellis 68 Head
Jonas Woller 24 Grandson
Mary Woller 20 Granddaughter
Elizabeth Woller 19 Granddaughter
John Woller 2 Grand Daur Child
Eliza Woller 4 Mo Grand Daur Child
I think Elizabeth Lancaster (nee Ellis) might be great aunt of Mary Ann
In 1841 Jonas and his two sisters (listed as Wealer) are again with grandfather Joseph Ellis at Faweather
This is an interesting marriage
John Whalley of Naple-ing
Ann Ellis of Faweather
Marriage Date 19 Nov 1827 Bingley, All Saints,
Witness William Lancaster