Lillian was born in 1878. She passed away in 1972. 
↑ U.S., Social Security Death Index, 1935-2014 Number: 142-16-0302; Issue State: New Jersey; Issue Date: Before 195
Find A Grave, database and images (https://www.findagrave.com : accessed 19 June 2018), memorial page for Dr Lillian Evelyn Moller Gilbreth (24 May 1878–2 Jan 1972), Find A Grave Memorial no. 30391704, ; Maintained by Find A Grave Cremated, Ashes scattered at sea, who reports a ashes were scattered in the waters off Nantucket..
1920 census - "United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M45K-2Y6 : accessed 27 November 2018), Lillian Gilbreth in household of Frank Gilbreth, Montclair Ward 3, Essex, New Jersey, United States; citing ED 83, sheet 6A, line 36, family 113, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, 1992), roll 1030; FHL microfilm 1,821,030.
1930 census - "United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:X4NC-RWV : accessed 27 November 2018), Lillian M Gilbreth, Montclair, Essex, New Jersey, United States; citing enumeration district (ED) ED 533, sheet 14A, line 30, family 262, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 1332; FHL microfilm 2,341,067.