Henry Smith and Lydia Critchit married on 25 Mar 1790 possibly in Sanbornton, Belknap, New Hampshire.
Buried in Joshua Lane Burial Ground, Tilton, Belknap County, New Hampshire. 
↑ "New Hampshire Marriage Records, 1637-1947," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FLFP-C24 : 26 September 2017), Henry Smith and Lydia Critchit, 25 Mar 1790; citing , Bureau of Vital Records and Health Statistics, Concord; FHL microfilm 1,001,304.
↑ Find A Grave: Memorial #83351502 in Joshua Lane Burial Ground, Tilton, Belknap County, New Hampshire, USA. Transcription error of gravestone. It says she died in 1844 aged 70 which would make her birthyear 1774.
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It may be possible to confirm family relationships with Lydia by comparing test results with other carriers of her ancestors' 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 Lydia: