One needs to be suspect with spellings in genealogical work. I believe the two Lewis Baughs in these two census to be one and the same. Note the brother's initials also.

1860 United States Federal Census about Lewis B Baugh
Name: Lewis B Baugh
Age in 1860: 15
Birth Year: abt 1845
Birthplace: Alabama
Home in 1860: District 2, Limestone, Alabama
Gender: Male
Post Office: Athens
Value of real estate: View image
Household Members:
Name Age
James B Baugh 30
Lewis B Baugh 15
John M Baugh 18
Richard T Baugh 13

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1880 United States Federal Census about Lewis C. Baugh
Name: Lewis C. Baugh
Home in 1880: District 9, Giles, Tennessee
Age: 35
Estimated birth year: abt 1845
Birthplace: Alabama
Relation to Head of Household: Brother
Father's birthplace: Tennessee
Mother's birthplace: Tennessee
Neighbors: View others on page
Occupation: Laborer
Marital Status: Single
Race: White
Gender: Male

Household Members:
Name Age
R. I. Baugh 33 Head of Household, born in Alabama, Farmer, father born in Tennessee
Fannie E. Baugh 26
Edward Baugh 6
Lizzie Baugh 4
Charles Baugh 3
Lewis C. Baugh 35 Laborer, brother of Head of household
William Bowers 14
Anna Bowers 12
Hanibal Bailey 25