In 1871, Lucy Day is a 50 year old charwoman, widow, born Douglas, lodging with a Thomas Fargher family in Back Strand Street. Thomas Fargher age 52 is a roper, born Castletown, with wife Elizabeth, age 44, born Douglas.
Conchan E District 10a page 19

So it looks as though the 1851 census taker made some errors. Lucy nee Kelly was born in Douglas, and Richard Day was born in Bootle.