Barbara (Unknown) was born about 1620, based on the birth of her first known child in 1642, and she was probably born in England. Her parents and immigration year are not known.
"Barberie" married Andrew Lister/Lester in Gloucester, Massachusetts Bay Colony, about 1641[1][2].
The list of children below follows Avery's History of the Town of Ledyard 1650-1900[3], and the town records of Gloucester.
Children of Barbara and Andrew, all born in Gloucester[1].
The Lester family moved to what was then called Nameaug or Pequot, about 1651, following their minister from Gloucester. New London did not become the official name of the town until 1658. Barbara died in Nameaug / New London on 2 February 1653/4[1], the first recorded death of a woman in the town.
Her marriage to Andrew Lester so shortly after the removal of the Blinman Party to Gloucester suggests that she was one of one of the original Blinman Party members, possibly someone's daughter or relative. See The Blinman Party and The Cape Ann Company for details.
Barbara's son Andrew married Hannah Bradley, who was a Mayflower descendant. It is possible that Barbara is sometimes given a Bradley surname due to confusion with Hannah. None of the standard sources for Barbara even hazard a guess as to her surname or family; the "Bradley" surname for her seems to be one of those Internet things. See FamilySearch for an English parentage for Barbara, presented entirely without proof. In the absence of any records for her birth surname, her LNAB has been changed to Unknown.
Note that Savage's account of Andrew Lester's wives and children contains several errors.
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