After adding the Burns name, Ancestry (I claim no credit) through up a coincidental suggestion
1851 census in Lancaster
Andrew Burns 29 b Roscommon, Ireland
Jane Burns 29 b Roscommon, Ireland
Mary Burns 8 b Wigton, Cumberland
Margaret Burns 6 b Preston, Lancashire
Now this doesn't tie up with the 1871 census as although Mary Smith nee Burns shows at the right age (1843 birth), it shows her being born in Ireland.
Just an interesting one for the mix.