It's commonly accepted that Lydia Wilson's maiden name was Welch, but I cannot find concrete evidence of this.
We know from the 1865 Census that Lydia Wilson was born in Vermont around 1790. There is indeed a Lydia Welch born in Pownall, Vermont, in 1788, but I can't confirm that they are the same person.
Notably, Lydia Wilson's age at death listed on her gravestone points to a birthdate of 18 September 1790, while the birthdate of Lydia Welch in Vermont was 19 October 1788.
Sources
"New York State Census, 1865," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVNN-GY46 : 8 March 2021), Lydia Willson in household of Benjamin W Willson, , Sardinia, Erie, New York, United States; citing Census, p. 6, citing multiple county Clerks; Warren and Lewis County Board of Supervisors; multiple counties in New York; Utica and East Hampton Public Libraries, New York.
Find a Grave, database and images (https://www.findagrave.com/memorial/18514682/lydia-wilson: accessed 12 October 2022), memorial page for Lydia Wilson (18 Sep 1790–1 Jun 1868), Find A Grave: Memorial #18514682, citing Greenvale Rural Cemetery, Fairport, Monroe County, New York, USA; Maintained by Frederick Porter (contributor 48254596) .
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