Dear Mr. Bynum,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Population Schedules for the 1880 Census, the Population Schedules for the 1890 Census; the Population Schedules for the 1900 Census, and the Population Schedules for the 1910 Census, the Population Schedules for the 1920 Census, the Population Schedules for the 1930 Census, and the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that may contain information about your mother and her family in Arkansas and Missouri. The 1940 Census schedules are digitized and available using the Catalog. See NARA’s 1940 Census Records web page for more information. For access to the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at firstname.lastname@example.org.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
For information about the U.S. Census, see the Census Bureau technical documentation and questionnaires.
You may wish to search Ancestry.com or FamilySearch.org for the U.S. Census. There may be a fee for using Ancestry. Instead, check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
We suggest you search the Arkansas Births and Christenings, 1812-1965 index, the Arkansas, County Marriages, 1837-1957, the Arkansas Church Marriages, 1860-1976, and request your mother’s marriage certificate from the Arkansas Department of Health. We also suggest you search the Missouri Death Certificates, 1910 - 1969 index for records of the Lawson side of your family.
We hope this is helpful. Best of luck with your family research!
You might recognize the resources suggested by Cara as common and useful databases used in genealogy. If genealogy is new to you, I'd suggest looking for a genealogy group in your area to join. Hobbyist genealogists are typically highly enthusiastic about genealogy and excited to help newcomers. These groups are often associated with public libraries or county genealogy museums.
As for specific searches on your relatives, I did some quick searches and found that Alonzo Butler was the easiest to trace and I'd suggest starting with him.