This 1880 census record with Lee is the only record I have for Lee as a child assuming the birth year was not correct in the 1910 census I found for Lee. I can't reliably state these two Lee's are the same without another reference as the birth year is about 7 years off.
What I think I need is possibly a 1900 census record with Lee or a record that shows Lee as a relative of any other of Larkin's children.
"United States Census, 1910," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MGX5-34C : accessed 15 February 2019), Lee Paul, Civil District 5, Carter, Tennessee, United States; citing enumeration district (ED) ED 5, sheet 11B, family 221, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 1492; FHL microfilm 1,375,505.