From the census data I looked up the births of dau Mary A and Katherine T Lynch and found these 2 girls were the dau of James P Lynch and Hannah T Mahoney.This Hannah died in 1911 as did another infant dau Theresa Ann/Ann Theresa Lynch. Did not find a marriage of Helen Jenkins to James P Lynch nor could I find a death cert for her husband Walter B Heintz, but if they were living in RI, might not be on line. The James P Lynch that married Hannah - is the son of Michael and Mary (Harkins) Lynch who appears to match the birth of your James P b. Feb 4, 1875 son of Michael and Mary (H) Lynch.Will require further confirmation but a good place to start.
All from familysearch.org- some images such as marriages and death records can be viewed, saved, printed etc.
Not my family - Good Luck
U S Census, 1920Sommerville City Ward 1 Precinct 4, Middlesex, MA
selfJames P LynchM 44y Massachusetts wifeHelen M Lynch F 34y Massachusetts dauKatherine T Lynch F 16y Massachusetts dauMary A Lynch F 12y Massachusetts Stepson Charles A Hentz M 11y Massachusetts Stepdau Isabelle G Hentz F 9y Rhode
Catherine Teresa Lynchfemale Address 4 George St, Boston Birth22 Jun 1903Boston, Suffolk, MA father: James P. Lynch birthplace Charlestown mother: Hannah Mahoneybirthplace: Charlestown
Mary Agnes Lynch female Address 5 George St, Boston Birth19 Nov 1907Boston, Suffolk, MA father: James P Lynchbirthplace Charlestown mother: Hannah T Mahoney birthplace Charlestown
Theresa Anna Lynch Address 2 Caldwell St Birth21 Oct 1910Boston, Suffolk, MA father: James P Lynchbirth Boston mother: Hannah Mahoney birth Boston
Massachusetts, Marriages name:James P. Lynch Address 2 Caldwell St. Male Age 27 estbirth 1875 Boston marital status 1st father Michael Lynchmother Mary Harkins Marriage 11 Jun 1902 Boston, Massachusetts marriage registration year 1902 marriage registration place Boston, MA (105 no. 2414) Official:John J Driscoll, PR, 303 Bunker Hill St. spouse Hannah T. Mahoney Address4 George St. Female Age 27 est birth 1875 Boston marital status 1st fatherJames F. Mahoneysmother Catharine Mccabe
Massachusetts, Deaths https://familysearch.org/pal:/MM9.1.1/N48K-RFJ name: Hannah T Lynch Address 2 Caldwell St Death24 Feb 1911Boston, MA BurialHoly Cross,, Malden, MA FemaleMarried Age 36 birthplace: Boston, Massachusetts father: James MahoneyBirthplace Ireland mother: Catherine MccabeBirthplace Ireland spouse: James P Lynchbirthplace Boston
https://familysearch.org/pal:/MM9.3.1/TH-267-11777-76189-17?cc=1463156&wc=12502772 name: Anna T Lynch Address 2 Caldwell Street Death04 Aug 1911 : Boston, MA Burial Holy Cross, Malden, MA Female age:0 yrs birth date: 1911Boston, MA estimated birth year: 1911 father: James P Lynchbirth Charlestown mother: Hannah Mahoney birth Charlestown
Massachusetts, Marriages name: Walter B. Hentz Marriage18 Dec 1901 : Hyde Park, MA Male age 27Widowed birthplace: Boston est birth1874 father: James B.mother: Margaret Harrington spouse: Helen M. Jenkins Age 16 BirthplaceNova Scotia marital status: Single father: Frank W.mother: Lenora Campbell