He probably was about 1735, but there is no birth record at Marshfield. Bertha Bortle Beal Aldridge, "Laphams in America: Thirteen Thousand Descendents Including Descendents of John from Devonshire, England, to Providence, R.I., 1673: Thomas from Kent, England, to Scituate, Mass., 1634: and Genealogical Notes of Other Lapham Families"
(Victor, NY?: n.p., 1953?), p. 409, shows him as son of Joseph and Abigail (Joyce) Lapham, born at Marshfield but with no date. Attached are the pages from that book showing his descent from Thomas Lapham, along with the title page

Pembroke [Pembroke VR 174], Jan Oldham, "Magoon On-Line Database," Dec 2002

d. aft. 8-Sep-1812

Mercy, d. Jesse and Mercy, Sept. 3, 1763." (Pembroke VR page135)

Vital Records of Marshfield, Massachusetts to the Year 1850 by Robert M. and Ruth Wilder Sherman, 1969, page 405 gravestone record, 73-85851