James Lackey in the 1870 census NY, NY... 

The only thing that throws me off is the age given for James (40), when we have other doc showing he was b in 1838 (other census doc). But...all the other names match up. Ages match, give or take a few years. Both Elizabeth and Frances are listed with their pet names. Jane wasn't born until 1876 in CT 
James Lackey found in:
Census Microfilm Records: New York, 1870 
Age: 40 
Gender: M 
Race: W 
Birthplace: IREL 
State: New York 
County: NEW YORK 
Locale: 11-WD 19-E D 
Series: M593 
Roll: 988 
Part: 1 
Page: 453A 
James Lackey, 40, M, W, Blacksmith, b in Ire, m&f born of foreign tongue
Jane Lackey, 40, F, W, b in Ireland, m&f born of foreign tongue
Samuel Lackey, 11, M, W, at school, b in Ire, m&f born of foreign tongue
John Lackey, 9, M, W, blank at school?, b in Ire, m&f born of foreign tongue
Fannie Lackey, 7, F, W, blank at school?, b in Ire, m&f born of foreign tongue
Rebecca Lackey, 5, F, W, blank, b in NY, m&f born of foreign tongue 
Lizzie Lackey, 3, F, W, b in NY, m&f born of foreign tongue