William Henry Harrison Lampton Jr. appears to be one and the same as William L Harrison described above. On the muster card into Purcell's Company he is listed as 25 yrs old making dob abt 1836.

Boone County Census 1860 note rocky fork where Purcell hit the jackpot...
Name: Wm H H Lampton
[William Henry Harrison Lampton]
Age: 24
Birth Year: abt 1836
Gender: Male
Birth Place: Missouri
Home in 1860: Rocky Fork, Boone, Missouri
Post Office: Columbia
Dwelling Number: 267
Family Number: 259
Household Members:
Name Age
Wm Lampton 56
Martha Lampton 49
Wm H H Lampton 24
Mary H Lampton 13

in 1850
Name: Harrison Lampton
Gender: Male
Age: 14
Birth Year: abt 1836
Birthplace: Missouri
Home in 1850: District 8, Boone, Missouri, USA
Attended School: Y
Line Number: 18
Dwelling Number: 677
Family Number: 677
Household Members:
Name Age
William Lampton 46
Martha Lampton 32
Jane Lampton 16
Harrison Lampton 14
Louiza C Lampton 11
Mary Lampton 2

in school 1857
Name: William H H Lampton
Publication Year: 1857
Publication Place: Missouri
School Name: University of the State of Missouri
Residence Place: Boone County, Missouri

1863 draft record
Name: Wm H H Lampton
Birth Year: abt 1837
Place of birth: Missouri
Age on 1 July 1863: 26
Race: White
Marital status: Unmarried (Single)
Residence: Rocky Fork, Boone, Missouri
Congressional District: 9th
Class: All

1870 census
Name: Wm H Lampton
Age in 1870: 34
Birth Year: abt 1836
Birthplace: Missouri
Home in 1870: Township 49, Boone, Missouri
Race: White
Gender: Male
Post Office: Sturgeon
Occupation: Farmer
Cannot Read: Y
Cannot Write: Y
Male Citizen over 21: Y
Inferred Mother: [No Name]
Household Members:
Name Age
Wm H Lampton 34

1880 census
Name: William H. Lampton
Age: 43
Birth Date: Abt 1837
Birthplace: Missouri
Home in 1880: Columbia, Boone, Missouri, USA
Dwelling Number: 103
Race: White
Gender: Male
Relation to Head of House: Self (Head)
Marital status: Married
Spouse's name: Carrie V. Lampton
Father's Birthplace: Kentucky
Mother's Birthplace: Kentucky
Occupation: Farmer
Neighbors: View others on page
Household Members:
Name Age
William H. Lampton 43
Carrie V. Lampton 33
Henryeta Lampton 13
William A. Lampton 11
Fannie H. Lampton 9
Jennie Lampton 7
John Lampton 5
Birdie Lampton 1

Marriage to Carrie Sims 1866
Name: William H. H. Lampton
Spouse: Carie Sims
Marriage Date: 13 Feb 1866
County: Boone
State: MO

Finda grave record https://www.findagrave.com/memorial/65357715
Name: William Henry Harrison Lampton
Birth Date: 12 Sep 1836
Birth Place: Missouri, United States of America
Death Date: 27 Nov 1892
Cemetery: Centralia Cemetery
Burial or Cremation Place: Centralia, Boone County, Missouri, United States of America
Has Bio?: Y
Mother: Martha Lampton
Spouse: Caroline Virginia Lampton
Children: William Ashley Lampton