Joseph A. Lawrence was the youngest child of Joseph Lawrence, who had settled for a short time at Cayuta Lake before his early death, and of Mary Sackett of the longstanding Sackett family of Newtown. Joseph spent his life in Newtown, Long Island, which later became part of the Borough of Queens, New York City, upon consolidation in 1898. He engaged in the lumber business, a trade of increasing importance as Long Island developed during the mid-nineteenth century.

Lawrence took an active role in local civic affairs. A Republican in politics, he served as Receiver of Taxes for the town of Newtown and also held other minor local offices, including Town Auditor and School Trustee. Contemporary notices described him as a useful and public-spirited citizen who took an interest in the management and improvement of local affairs. He died in 1889 and was buried in Maple Grove Cemetery, Kew Gardens, Queens, New York.