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).
He worked for the Illustrated London News (from 1880), Fun (from 1893), Judy and John Bull, and illustrated a number of books, including Father Bunny's Secret by his wife Emily Nichols. His books include The Picadilly Peepshow (1879), satirising the 1879 Royal Academy exhibition, and The Home Rule Pill (1893), attacking Gladstone's Irish Home Rule bill.
In financial difficulties, he committed suicide in 1907.
- B. P. Bowen, "Dublin Humourous Periodicals of the 19th Century", Dublin Historical Record Vol 13 No 1, 1952, pp. 2-11
- Mark Bryant, Dictionary of Twentieth Century British Cartoonists and Caricaturists, Ashgate, 2000, p. 146