I believe I have found your Levi DAVIDSON in the 1880 census. There were 25 Levi Davidsons in the nation but he was the only one born and found in TN. Now you have an approx. year of birth for him. I copied the neighboring household next door to Levi's - the individuals were also named DAVIDSON. You will note that their race was reported as white and Levi's as black. I have read that many slaves took the surnames of their masters - so perhaps Levi's father was a slave on a DAVIDSON plantation. I have supplied this second census because it may provide clues if you try to search your DAVIDSON surname backwards in time. I am going to continue looking in another census records and will post more for you tonight.

1880 Census Place: District 10, Lincoln, Tennessee
Source: FHL Film 1255267 National Archives Film T9-1267 Page 139A
Relation Sex Marr Race Age Birthplace
Geo. M. DAVIDSON Self M M W 36 TN
Occ: Farmer Fa: --- Mo: ---
Susania A. DAVIDSON Wife F M W 22 TN
Occ: Keeps House Fa: --- Mo: ---
James R. DAVIDSON Son M S W 8 TN
Occ: At School Fa: --- Mo: ---
Ida DAVIDSON Dau F S W 5 TN
Occ: At School Fa: --- Mo: ---

1880 Census Place: District 10, Lincoln, Tennessee
Source: FHL Film 1255267 National Archives Film T9-1267 Page 139A
Relation Sex Marr Race Age Birthplace
Elijah DAVIDSON Self M M B 55 TN
Occ: Farmer Fa: --- Mo: ---
Jane DAVIDSON Wife F M B 53 TN
Occ: Keeps House Fa: --- Mo: ---
Alec DAVIDSON Son M S B 19 TN
Occ: On Farm Fa: --- Mo: ---
Tennessa DAVIDSON Dau F S B 11 TN
Occ: At Home Fa: --- Mo: ---
Levi DAVIDSON Son M S B 12 TN
Occ: At Home Fa: --- Mo: ---