The article (above) suggested Andrew Bates (brother of James Bate, of Dorchester & Clement Bate of Hingham) as a possible father for Elizabeth Lawrence However, that was debunked at https://www.werelate.org/wiki/Person:Elizabeth_Unknown_(4206) : Since it was generally held that Edward Bates was a brother to James Bates of Dorchester, and since the widow returned to Dorchester, naturally this turned into the assertion seen everywhere that Elizabeth was sister or daughter of James Bates of Dorchester. However, modern research shows that Edward Bates is not the brother of James Bates of Dorchester. Waters' presentation (see the link embedded in the Torrey citation, p. 1302) of the Bates family in Lydd, England shows that that Edward, brother of James, was buried in 1616. [Before Elizabeth’s estimated birth date of 1618.].
WeRelate further notes: > “The question remains, was Elizabeth the sister, or sister-in-law of Edward Bates. According to the TAG article, p. 65:94, Edward has a sister Elizabeth, bp. 1604, "poss. the Elisabeat Beate who m. Aston Clinton 30 Sep 1629 Walter ["Water"] Warde". Susanna Putnam, p. 65:96, has a sister Elizabeth, bp. 1612, "living 10 Nov. 1625 (father's will)". The latter seems a more likely age for the wife of Thomas Lawrence.
https://www.wikitree.com/wiki/Bates-736
James Bate and Alice Glover are featured in Great Migration 1634-1635, A-B by Robert C. Anderson, and there is no daughter named Elizabeth. (see "father" James Bates-732 for a link)
Anderson, Robert Charles, (1995) "James Bate," featured name. Great Migration 1634-1635, Vol I, A-B. AmericanAncestors.org NEHGS (Vol A-B, Pages 199-201) < AmericanAncestors >
Also tagging Dean Richard Hobart for a look / see. He’s done a lot with Hingham families.