Father Obadiah Moore, mother variously spelled Emma, Eunice.
Sources
"Massachusetts Births and Christenings, 1639-1915," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F4DN-HSZ : 4 December 2014), Lucy Moore, 03 Nov 1748; citing Sudbury, Middlesex, Massachusetts, p 94; FHL microfilm 185,455.
"History of the Town of Marlborough - Cheshire County, New Hampshire" by Charles A. Bemis, originally printed in 1881 by the Press of Geo. H. Ellis, Boston, Ma., new edition printed by The Frost Free Library, produced by the New England History Press, Somersworth, NH. Copyright 1974 (p.555)
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DNA Connections
It may be possible to confirm family relationships with Lucy 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 Lucy: