Lydia was born about 1669 in Newport, Rhode Island to George Gardiner and 3rd wife Lydia Ballou. When her dad died in 1677 Lydia, her mom and brothers Robert and Peregrine went to Providence RI, where Lydia married Joesph Smith on April 4, 1689. Joseph was a weaver, they spent their lives in Providence. They had 6 sons and 3 daughters. Lydia died in 1723 her husband probably married again he lived until 1749.

Lydia and her children through her dad (3) and mom’s (2) marriages are connected to the Angell, Arnold, Ballou, Gardiner, Hawkins, Olney, Smith, Tefft and Whipple families.

Source
Marriage Volume 2 page 77 image 121 of 444 , a family register for the people by Arnold. At FamilySearch.org

Lydia Gardiner (1669 – 1723)
Israel Smith (1689 – 1726)
Naomi Smith (1720 – 1799)
Israel Angell (1740 – 1832)
Asa Angell (1771 – 1842)
Dexter Angell (1794 – 1854)
Delia Viola Angell (1839 – 1916)
Matilda Flood (1858 – 1940)
Philippa Flood Mockford (1891 – 1979)
Elizabeth Speedy (1917 – 2005)