Daniel is probably the son of Nathaniel Coulter IV and Catherine Strunk. I found Nathaniel and Catherine in the 1850 census; however, Daniel and Lydia were already married living in a neighboring county.
The history that's been handed down to me is this (and if anyone can give me some additional sources, I'll add it to the tree)
Daniel
son of Nathaniel and Catherine Strunk
son of Nathaniel III and Gabella Coulter (1/2 second cousins)
son of Nathaniel II and Grizzell Lough
son of Nathaniel I and Janet (immigrant ancestor from Ireland)
son of John Coulter born in Scotland
son of Nathaniel Coulter
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