Lawrence's parents were Unitarians, but he became Anglican and was confirmed as a member of St. Paul's Episcopal Church in Boston in 1842. He met and married Sarah Elizabeth Appleton (1822–1891) at the church. Sarah was a daughter of U.S. Representative William Appleton and Mary Ann Appleton (née Cutler). His mother was a relative of Samuel Appleton, a trustee of Massachusetts General Hospital and president of the Young Men's Benevolent Society.