Lucretia was born about 1795. Lucretia Latham ... She passed away in 1891.
Ruby Williams posted a lengthy message at genealogy.com (source below) in February 2012 regarding Lucretia and her marriages. It would appear from information contained in this message that Lucretia either divorced or deserted Belaver. It also appears from this that, when her father's estate was probated, her family was unaware that they were no longer married and perhaps did not even know where she was.
Sources
"United States Census, 1840," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHB6-YDW : 24 August 2015), Lucretia Nichols, Morgan Township, Owen, Indiana, United States; citing p. 105, NARA microfilm publication M704, (Washington D.C.: National Archives and Records Administration, n.d.), roll 89; FHL microfilm 7,728.
Maternal relationship is suggested with an AncestryDNA test match between Philip Capobres GEDmatch A880062, Janice Hobson GEDmatch A663300 , and Thomas Anderson GEDmatch A486051 sharing a 32.2 cM on chromosome 19 from 40,627,844 to 58,272,963
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DNA Connections
It may be possible to confirm family relationships with Lucretia by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Lucretia:
Parental relationship has been changed from confirmed with DNA to confident because using matching DNA from 2 siblings and a distant cousin is not an approved method of triangulation on WikiTree. See this page that states If a relationship is supported with DNA evidence but cannot be considered confirmed using one of the approved methods use the Confident status instead of Confirmed with DNA.: https://www.wikitree.com/wiki/Help:Confirmed_with_DNA#Genealogy_Supported_by_DNA_but_not_Confirmed_with_DNA