Lawrence was born in Melbourne. She won a number of vocal competitions in her teens, and went to Paris to study under Cécile Gilly. In 1932 she made her operatic debut in Monte Carlo as Elisabeth in Wagner's Tannhauser. In 1933 she made her first appearance at the Paris Opera, playing Ortrud in Lohengrin, and in the same year she sang in the world premiere of Joseph Canteloube's Vercingétorix.
In 1935, she made her debut at the Metropolitan Opera in New York City playing Brunnhilde in Die Walküre, and the following year played the immolation scene in Götterdämmerung by riding her horse into the flames as Wagner had intended, making her one of the few, possibly the only, soprano to do this.
During a performance in 1941 in Mexico, she found herself unable to stand. She discovered that she had polio, and was left in a wheelchair as a result. She attempted to make a return to the stage, but was hampered by her lack of mobility. A performance as Amneris in Giuseppe Verdi's Aida in Paris in 1946 was well received, but Lawrence retreated from the stage, and instead began to work as a teacher.
Although best known for her Wagner, Lawrence played in a range of other works, including Richard Strauss' Salome and less Wagnerian works such as Georges Bizet's Carmen. She made a number of recordings, mainly of works by Wagner. She was never regarded as such a great singer as her contemporary Kirsten Flagstad, but she received many good reviews, and it is generally thought they she would have continued to become more significant had she not suffered from polio.
A film was made about Lawrence in 1955, Interrupted Melody.