1860 US Census NY Cayuga Auburn W1 HH 508 1870 US Census NY Cayuga Auburn W1 HH 76
Lydia is first seen with John and Almira (in my to-date research) with John and Almira and siblings Clara and Charles in the 1860 US Census, enumerated as family 508 in Ward 1, Auburn, Cayuga County, New York, at age 10.
The same family grouping is seen in the 1870 US Census, same location, this time as family 76, Lydia age 20. I don't think there is any doubt that your relative is the Lydia in these records.
I am not personally related but have specialized research on the Heustis family. There is a chance that the Heustis family in Cayuga County descends from my wife's 5g-uncle Reuben Heustis, and then his wife Hannah, who lived in Pompey, Onondaga County from around 1800-1812. I think I have found Hannah in Owasco, Cayuga County, in the 1820 US Census. Later I believe that she was located in Crawford County, PA with at least three of her children. However that is somewhat speculative - even the identification of that Reuben in Pompey is not proved.