Even thou she used Young as her surname to marry Lawson, Young might not be her maiden name, which is usually used when you marry even if you have children from a precious marriage.
Did Lawson adopt or just change the names of Bertha & Lennie?
And I assume she went by the name of Belle and not used Ella on any records?

1910 census
Name: Bertha M Lawson
Age in 1910: 8
Birth Year: 1902
Birthplace: Arkansas
Home in 1910: Union, Jackson, Arkansas
Race: White
Gender: Female
Relation to Head of House: Daughter
Marital Status: Single
Father's Name: Robert Lawson
Father's Birthplace: Arkansas
Mother's Name: Belle Lawson
Mother's Birthplace: Arkansas
Neighbors: View others on page
Household Members:
Name Age
Robert Lawson 28
Belle Lawson 25
Bertha M Lawson 8/1902
Linnie B Lawson 6/1908
Source Citation: Year: 1910; Census Place: Union, Jackson, Arkansas; Roll: T624_53; Page: 9B; Enumeration District: 0071; FHL microfilm: 1374066.
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1920 census
Name: Robert Lawson
Age: 46
Birth Year: abt 1874
Birthplace: Tennessee
Home in 1920: Union, Jackson, Arkansas
Race: White
Gender: Male
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Belle Lawson
Father's Birthplace: Tennessee
Mother's Birthplace: Tennessee
Home owned: Rent
Able to Read: Yes
Able to Write: Yes
Neighbors: View others on page
Household Members:
Name Age
Robert Lawson 46/1874
Belle Lawson 30/1890
Lennie Lawson 16/1904
Viola Lawson 9/1911
Lillian Lawson 1/1919
Source Citation: Year: 1920; Census Place: Union, Jackson, Arkansas; Roll: T625_66; Page: 4B; Enumeration District: 69; Image: 977.
----------------------------------------------------------
ARKANSAS MARRIAGES
Name: Robert Lawson
Age: 30 / Birth Year: abt 1879
Residence: Newport, Jackson, Arkansas
Spouse's Name: Belle Young
Spouse's Age: 24 / Birth Year; abt 1885
Spouse's Residence: Newport, Jackson, Arkansas
Marriage Date: 19 Sep 1909
Marriage License Date: 18 Sep 1909
Marriage County: Jackson
Event Type: Marriage
FHL Film Number: 1290125
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2 possibilities for her marriage to a "YOUNG"
these are in Pope county, long way from Jackson co.
arkansas marriages
Name: John Young
Spouse: Ella Granmon
Marriage Date: 25 Dec 1899
County: Polk
State: AR
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Name: W. S. Young
Spouse: Bell Griffin
Marriage Date: 11 Feb 1900
County: Pope
State: AR
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check with familysearch.org to see if you can find any more information
good luck in your search