Don't know how much new information this will be but what I found on this family in the Lillibridge book is as follows:
Joseph T. Lillibridge born 1830, Exeter, Washington co., RI, Died April 28, 1891, Cranston, Kent Co., RI.Shows up in a number of RI censuses.Wife, Louisa (Rhodes), born about 1834, Warwick, Kent Co., RI.Children:EDWARD S., Florence E., Mary A., Lottie (Charlotte?) A., Jesse A., Eva Amanda.Considerable research has not determined his parents.
EDWARD S. Lillibridge born about 1862, RIMarried Annie Mayne on July 19, 1885, Kingstown, Washington Co., RI.Was in the 1900 census in Washington co., South Kingstown, RI.Children:Florence E., Lottie (Charlotte?)A., Jesse A., Eva Amanda.
It seems strange that Joseph and Edward have children with almost the exact same names.Perhaps the children listed for Joseph, with the exception of Edward, are actually the children of Edward.