Alexandra Luke was born Margaret Alexandra Luke on May 14, 1901, in Montreal, Quebec. She was one of twin daughters born to Jesse Herbert Ritson Luke and Emma Russell Long. The family moved to Oshawa, Ontario in 1914, where Luke attended public and high schools. After finishing high school, she and her twin sister Isobel trained as nurses at the Columbia Hospital for Women in Washington, D.C., graduating in 1924. Luke returned to Oshawa and married Marcus Everett Smith in 1925, but he died suddenly four months later. She gave birth to their son, Richard, in 1926. In 1928, she married Clarence Ewart McLaughlin, grandson of Robert McLaughlin, founder of the McLaughlin Carriage Company. The couple had a daughter, Mary, in 1930.

Luke began painting in her late twenties, initially as a self-taught artist. Inspired by local artists Dorothy Van Luven and Dorothy Henderson, she started organizing children's art classes and contributed to building Oshawa's arts community. She became a member of several organizations including the Oshawa Women's Lyceum Club and the Oshawa Historical Society. With Dorothy Van Luven, she organized 69 exhibitions at the YWCA's Adelaide House, many featuring abstract art. Luke painted landscapes in a Group of Seven-inspired style in a third-floor studio at Greenbriar, her home in Oshawa. She discovered abstract art around 1933 but did not begin painting abstractly until 1943.

In 1944, Luke sought a portfolio review from landscape artist Caven Atkins, who told her bluntly that her Group of Seven-inspired style was not viable, pushing her to explore abstraction further. In 1945, she enrolled in the Banff School of Fine Arts, studying under instructors including A.Y. Jackson, H.G. Glyde, and Jock Macdonald, with whom she developed a strong relationship based on shared interests in abstract art and spirituality. Based on the recommendation of artist Joe Plaskett, whom she met at Banff, Luke attended the Hans Hofmann School of Fine Arts in Provincetown, Massachusetts from 1947 to 1952, attending four of five summers. From Hofmann, she learned to create energy in her paintings through explosive color, thick impasto, and the use of white space.

Luke began exhibiting professionally in the early 1950s at venues including the Canadian Group of Painters and the Picture Loan Society, where she had a solo exhibition in 1952. That same year, she organized the first Canadian Abstract Exhibition, which opened at Oshawa's YWCA Adelaide House and toured across Canada to venues including Hart House at the University of Toronto and galleries in Windsor, London, Peterborough, Hamilton, Montreal, and Sackville, New Brunswick. The exhibition included nine Toronto and Hamilton-based artists who would become founding members of Painters Eleven. In 1953, Luke invited these artists to meet at her studio at Thickson's Point near Oshawa, leading to the formation of Painters Eleven. The group included Jack Bush, Oscar Cahen, Tom Hodgson, J.W.G. MacDonald, Ray Mead, Kazuo Nakamura, William Ronald, Harold Town, Walter Yarwood, Hortense Gordon, and Luke herself, making her one of two female founding members.

Luke painted under a pseudonym combining her middle and maiden names to distinguish herself from her sister-in-law, painter Isabel McLaughlin. She exhibited regularly with Painters Eleven until the group disbanded in 1960, participating in exhibitions in Montreal, New York, and Toronto. Between 1952 and 1966, her work was included in 80 group exhibitions as well as solo and two-person shows. Luke became a member of the Canadian Society of Painters in Water Colour in 1958, the Canadian Group of Painters in 1959, and the Ontario Society of Artists in 1960.

Luke's inner life was nourished by reading about art and spiritual thought, including Theosophy and works by P.D. Ouspensky. Around 1958, through Ouspensky, she learned of Gurdjieff and started a Gurdjieff study group in Oshawa, attending meetings of the Gurdjieff Foundation in Toronto and New York. Luke continued to paint and support abstract art until her death from ovarian cancer on June 1, 1967. Shortly before her death, she and her husband offered major financial support and works from their collection toward the creation of a public art gallery for Oshawa, which became the Robert McLaughlin Gallery in 1967. Luke donated the Alexandra Luke Collection of 81 paintings to the gallery, including many of her own works as well as pieces by the Group of Seven and members of Painters Eleven. Her work is held in collections including the Robert McLaughlin Gallery, the National Gallery of Canada, and the University of Alberta.