1J. H. Beers & Co., Representative Men and Old Families of Southeastern Massachusetts, Vol. 2, p. 607 (1912).
Apparently Lydia Cooke was married to John Faunce through 1732. Therefore she could not have been married to Samuel Leonard, as shown by numerous websites. In the absence of evidence for Samuel Leonard's wife I have opted to give the name Lydia without a maiden name.
"III) John Faunce, son of Joseph, born 1683, married in 1710 Lydia, born in 1685, daughter of Jacob Cooke, granddaughter of Jacob and Damaris (Hopkins) Cooke (the latter a daughter of Stephen Hopkins, of the "Mayflower," 1680), and great-granddaughter of Francis Cooke, of the "Mayflower," 1620. The children of John and Lydia (Cooke) Faunce were: Judith, born in 1711, who married Jabez Washburn; Lydia, born in 1714, who married Ebenezer Washburn; John, bom in 1716; Hannah, born in 1718, who married Charles Cook; Mary, born in 1720; Mehetabel, born in 1722, who married Thomas Cushman; and Rebecca, born in 1724, who married Tillson Ripley, of Plympton. The father married (second) in 1733 Ruth Sampson, and their only child was Mary, bom in 1734, who married Amos Curtis, of Scituate. He married (third) Lydia (Tilden) Cook, widow of Simeon Cook, and by this union had a son Benjamin, born in 1742."