He was the son of Joseph Lapham (1786–1851) and Anna (Keese) Lapham (1790–1833). In 1822, the family removed to Peru. On February 22, 1842, he married Jane R. Barker (1822–1869), and they had several children.
Later he married Hannah Barker, a niece of his first wife, and they had several children.
He was buried at the Quaker Cemetery in Au Sable, New York.
Lapham is a descendant of John Lapham (1677-1734) and his wife Mary Russell Lapham (1683-1752). His cousins through the Lapham family include Elbridge G. Lapham, a Congressman from New York, Roger D. Lapham, a mayor of San Francisco, California, Christopher Lloyd, an actor, and Susan B. Anthony, Women's Rights Activist.
- The New York Civil List compiled by Franklin Benjamin Hough, Stephen C. Hutchins and Edgar Albert Werner (1867; pg. 442)
- Biographical Sketches of the State Officers and Members of the Legislature of the State of New York by William D. Murphy (1861; pg. 73ff)
- Book of Appendices to the History and Genealogy of the Ancestors and Some Descendants of Stukely Westcott, 1592-1677 by Roscoe Leighton Whitman & Jonathan Russell Bullock (1939; pg. 124)