By logic this Benjamin Rupert born 1860 could not be the father of Lizzie Rupert as they were same age. The obituary of Hattie Harman states she lived with her grandparents at time of death in 1902. More to the story

Listed twice in 1880 -census
In 1880 in house of Daniel Stauffer listed as daughter, single but as Lizzie Harmon.
This is very confusing as she married Harmon in 1879
Also listed with spouse Francis Harman in Fairfield Twp Columbiana near
( sge may be related to Caldwells
Celestie Caldwell Abt 1858 Ohio 1880 Fairfield, Columbiana, Ohio, USA
Alice L. Caldwell Abt 1879 Ohio 1880 Fairfield, Columbiana, Ohio, USA
Francis Harman Abt 1854 Ohio 1880 Fairfield, Columbiana, Ohio, USA
Lizzie Harman Abt 1861 Ohio 1880 Fairfield, Columbiana, Ohio, USA
Jonathan Varian Abt 1848 Ohio 1880 Fairfield, Columbiana, Ohio, USA
Amanda Varian Abt 1850 Ohio 1880 Fairfield, Columbiana, Ohio, USA

Maiden name may be Rupert
Find a Grave contributor, Deborah Himes has made the following suggested edits.
Lizzie Harman (50094163)

Suggested edit: Could the mother not be Lizzie rupert? I found a marriage license of Francis Marion Harman born: 12 Sep 1853 Columbiana County (son of Henry and Mary Ann Harmon buried next to Lizzie and Hattie) Columbiana County for Lizzie Rupert and Francis Harman. I found a letter from Hattie M Harman, dated Mon 23 May 1898, New Berlin Ohio to Grandma. (no envelope) She encloses photos (which were not with this letter copy) She tells of the upcoming commencement and Grandma coming and I am sending you photos of this letter. Because she sends a program to Blanche Rupert, Grace Vollnogle and Ella Lower. She talks about Aunt Henrietta and will Grandma go up and bring Grandma Snyder with her.. Francis Harmans FAG memorial 59635190.
Contributor: Deborah Himes (48275635) • [email protected]

This we know - Grace Vollnogle. Born about 1881 is d/o Peter Firestone Vollnogle
Blanch Rupert is d/o Benjamin Rupert

irths and Christenings Index, 1774-1973
Ohio, Births and Christenings Index, 1774-1973 No Image
Name: Lizzie Rupert
Gender: Female
Spouse: Francis Harman
Child: Hattie Harman
FHL Film Number: 931592
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w/o Francis ae 22y 7 m 8 d

She is found on 1880 census living with parents - perhaps Francis died?

United States Census, 1880 for Lizzie Harman
Name: Lizzie Harman
Residence: Fairfield, Columbiana, Ohio
Birthdate: 1861
Birthplace: Ohio, United States
Relationship to Head: Daughter
Spouse's Name:
Spouse's Birthplace:
Father's Name: Daniel Stauffer
Father's Birthplace: Ohio, United States
Mother's Name: Sarah Stauffer
Mother's Birthplace: Ohio, United States
Race or Color (Expanded): White
Ethnicity (Standardized): American
Gender: Female
Martial Status: Single
Age (Expanded): 19 years
Occupation: House Keeper
NARA Film Number: T9-1001
Page: 360
Page Character: A
Entry Number: 4412
Film number: 1255001
Household Gender Age
Parent Daniel Stauffer M 68
Parent Sarah Stauffer F 65
Lizzie Harman F 19

Trying to prove her identity
Others in this same plot Row 11:
Lizzie, Hattie, Mary Ann w/o Henry
Henry Harman
Freeman Harman s/o H & MA