The youngest of three sons of a Belfast clergyman, he and his journalist brothers, William and Joseph, moved to London, where Wallis began contributing to Punch in 1870. He also designed the masthead for the Illustrated Sporting and Dramatic News, for which he illustrated the "Capricious Critic" column, written variously by himself and his brother Joseph. He also contributed cartoons to the Dublin magazine Zozimus (1870-1872). In financial difficulties, he committed suicide in 1907.