Was Lizzie a second wife? According to the 1910 and 1920 census it looks like John E. was also enumerated as Johnnie.
Based on the approximate birth year of 1862, the 1870 census shows 2 results for John Cloud:

One in Madison Co., age 9, living with a Thomas & Matilda MANN and family and one in Macon Co., age 7, living with parents Sam & Amanda.

Based on the birth year again, could this be John E. in the 1880 census before he married?

Source Citation: Year: 1880Census Place: Beat 5, Madison, Alabama; Roll: T9_22; Page: 358C; Enumeration District: 229
Name: John Cloud
Home in 1880: Beat 5, Madison, Alabama
Age: 17
Estimated Birth Year: abt 1863
Birthplace: Alabama

T. W. Parker 33
Sarah E. Parker 33
James M. Parker 12
William L. Parker 7
Elisabeth Parker 4
George A. Parker 1
John Cloud, 17, Farm Laborer, AL, AL, AL

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Source Citation: Year: 1900
Census Place: Clouds Cove, Madison, Alabama
Roll: T623_29 Page: 2A; Enumeration District: 119
Name: John E Cloud
Home in 1900: Clouds Cove, Madison, Alabama
Age: 37
Birth Date: Jun 1862
Birthplace: Alabama

John E Cloud, 37, b. Jun 1862, married 8 yrs., AL, NC, VA, Farmer
Anjie E Cloud, Wife, 25, b. Mar. 1875, mother of 3 children, 2 living, AL, AL, AL
Clarance L Cloud, Son, 2, b. Mar. 1898, AL

If there's another child living, I don't know where it would be since there's only 1 child listed in the household. Maybe it was a mistake by the census taker.

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Source Citation: Year: 1910
Census Place: Clouds Cove, Madison, Alabama
Roll: T624_24; Page: 14A; Enumeration District: 140
Name: John E Cloud
Age in 1910: 48
Estimated Birth Year: abt 1862
Birthplace: Alabama

Clarkville & Hobbs Island Road
John E Cloud, Head, 48, married 19 yrs., AL, AL, AL, Farmer
Eliza Cloud, wife, 36, mother of 6 children, 4 living, AL, AL, AL
Clarance Cloud, Son, 12, AL, doesn't attend school, can't read or write
Jessie H Cloud, Son, 7, AL, doesn't attend school
Angy B Cloud,, Daughter, 5, doesn't attend school
Earl Cloud, Son, 2, AL

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Source Citation: Year: 1920
Census Place: Clouds Cove, Madison, Alabama
Roll: T625_31; Page: 14A; Enumeration District: 144
Name: Johnnie E Cloud
[Johnie E Cloud]
Home in 1920: Clouds Cove, Madison, Alabama
Age: 60 years
Estimated Birth Year: abt 1860
Birthplace: Alabama

Johnnie E Cloud, Head, 60, AL, AL, AL, Farmer
Lizzie Cloud, Wife, 44, AL, AL, AL
Jessie Cloud, Son, 17, attends school, AL, Farm Laborer
Angy Bee Cloud, Daughter, 16, attends school, AL
Earl Cloud, Son, Attends school, 11, AL
Vera Cloud, Daughter, Attends school, 9, AL
Bertie C Cloud, Daughter, 8, AL

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Source Citation: Year: 1930
Census Place: Clouds Cove, Madison, Alabama
Roll: 37; Page: 3A; Enumeration District: 36
Name: John Cloud
Home in 1930: Clouds Cove, Madison, Alabama
Age: 69
Estimated Birth Year: abt 1861
Birthplace: Alabama

John Cloud, Head, 69, doesn't own radio, age at first marriage: 26, AL, AL, AL, Laborer-General Farm
Lizzie Cloud, Wife, 55, age at first marriage: 17, AL, AL, AL
Jessie H Cloud, Son, 28, AL, Fisherman
Earl T Cloud, Son, 22, AL, Farm Laborer
Vera Mae Cloud, Daughter, 17, AL
Cristine Cloud, Daughter, 16, AL