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I have found an Archibald McPhatter (age 46) living in Gadsden County, Florida on the 1850 federal census. If he is the same as yours, though, Lucy is either no longer with him or has used a middle name.
Living in the home is Susan (age 27), John (age 6), and Christopher (age 3). Both Susan & Archibald were born in NC and the children in Florida. I do not find the elder Archibald in the 1860 Census, but I find a 16-year-old Archibald working as a laborer on the Arnold farm. (A William McFatter also worked there in 1850) A John A. McPhatter mustered in the 4th Florida Infantry on June 1861, so my assumption is that the child in 1850 must be John Archibald McPhatter.
In neighboring Jackson County I found my 13-year-old gggrandfather Austin McFatter. He was living with the Bryant Pittman family in 1850. My family has always wondered about our orphaned ancestor, but no one has ever figured out who his parents are. It is my assumption that Archibald & Susan are the missing parents. Perhaps the Christopher in the 1850 census is my Austin in 1860, but I have no proof. The family has always thought that he "made up" the name McFatter because the only McFatters we knew were Austin's decendents. Now that I have found Archibald, I am pretty certain that theory is wrong. I have been trying to follow the Pittman connection, thinking that perhaps Susan was a Pittman or maybe Bryant Pittman's wife Nancy was McPhatter before she wed. A lot of "perhaps" & "maybes", I know. I would love to know more about your Archibald, and If you would like a copy of the Census pages I have, I would be glad to attach them to an e-mail for you. Just let me know. Maybe we can help each other. Amy (email@example.com)