Joseph Edmund Wallis was born around 1837 in Alabama to Joseph and Elizabeth Wallis. His father was a farmer. The family moved to Washington County, Texas, sometime in the 1840s, and he attended the Chappell Hill Male Institute in the early 1850s. He worked as a merchant in Chappell Hill, Texas, and he also served as a local postmaster. He married Sarah Catherine Landes on January 12, 1860, and they had at least three children: Charles, born around 1861; Daniel, born around 1868; and Lockhart, born around 1879. By 1860, he was working as a farmer in Chappell Hill, and he owned $20,000 of real estate and $12,000 of personal property.
Wallis enlisted in the Confederate army on March 18, 1862, and he mustered in as a sergeant in Company B of the 20th Texas Infantry. He remained in the army until at least April 1863. He moved to Galveston, Texas, after the war, and he earned a living as a grocer. According to an early biographer, he was “closely identified with all [Galveston’s] commercial enterprises.” He served as a director of the Galveston City Company, vice president of the Galveston & Western Railroad Company, and a director of the Gulf City Cotton Press Company. He supported the Democratic Party, but he reportedly took “little interest in political affairs.” His wife died on September 11, 1902, and he died on October 4, 1907, in Houston, Texas.