Lawrence Casey was born in Rochester, New York, to Joseph Leo and Agnes Madeline (née Switzer) Casey. He studied at St. Andrew's Preparatory Seminary from 1919 until 1924, when he entered St. Bernard's Seminary. Casey was ordained to the priesthood on June 7, 1930. He then served as a curate at St. Mary's Church in Rochester until 1932, and was secretary to Bishops John Francis O'Hern (1932-1933), Edward Mooney (1933-1937), and James E. Kearney (1937-1946). He was named rector of Holy Cross Church in 1946 and of Sacred Heart Cathedral in 1952.

On February 10, 1953, Casey was appointed Auxiliary Bishop of Rochester and Titular Bishop of Cea by Pope Pius XII. He received his episcopal consecration on the following May 5 from Cardinal Francis Spellman, with Bishops Walter Andrew Foery and Alexander M. Zaleski serving as co-consecrators. Following the death of Bishop James Johnston Navagh, he was named Bishop of Paterson, New Jersey, on March 4, 1966. After eleven years as bishop, he resigned on June 13, 1977. Casey died just two days later, aged 71.