She was born Gertrude Alexandria Dagmar Lawrence-Klasen, of English and Danish extraction, in London, England, and was a professional performer by the age of ten. She was sent to Catholic convent schools and attended the Italia Conti Academy, presumably to keep her out of trouble. She understudied Beatrice Lillie in the Andre Charlot London revues in the 1920s and became the star when the revues were brought to Broadway in 1924 and 1926. She was one of the foremost comediennes of her day, capable of playing both slapstick clowns and elegant ladies. Her great charisma is attested to by those who saw her on stage, but her films struggle to convey her charm.

She married Francis Gordon-Howley, a director, in 1924, and they divorced in 1927. Lawrence had a daughter, Pamela, from this marriage. Lawrence then married Richard Aldrich, an American theatre owner from a blueblood family, on July 4, 1940, and they remained married until her death. In addition to an affair with film star Douglas Fairbanks Jr., she also had lesbian affairs, including a much-rumoured relationship with the British novelist Dame Daphne du Maurier, and apparently with Beatrice Lillie herself, who, when referring to Lawrence, said: "I knew her better than her husband". Passionate letters written between Lawrence and Du Maurier were published in a 1993 biography of Dame Daphne du Maurier, who long outlasted her one-time love interest. Lawrence also appears to have had a much earlier affair with du Maurier's own father, Sir Gerald du Maurier; in fact, Daphne du Maurier referred to Lawrence as "the last of Daddy's actress loves".

Lawrence's onstage persona inspired composers and writers. George and Ira Gershwin wrote the play Oh, Kay! for her, with the well-loved song "Someone to Watch Over Me". She was the first British actress to have a lead role on Broadway. Cole Porter wrote Nymph Errant for her to star in, and it opened in London in 1929. Noel Coward wrote Private Lives and Tonight at 8:30 (a cycle of nine one-act musicals and plays) for her. She starred as Liza Elliot in Kurt Weill and Ira Gershwin's psychoanalytical musical Lady in the Dark (played in the film version by Ginger Rogers), and was a popular entertainer of the troops in World War II.

She won the 1952 Tony Award for Best Actress for her role as Anna Leonowens in The King and I by Rodgers and Hammerstein.

Lawrence died of liver cancer, which caused her to suffer jaundice, in New York, New York at the age of only 54, and she was buried in her pink "Shall We Dance?" gown from the second act of The King and I, in Lakeview Cemetery, in Upton, Massachusetts.

In the biographical 1968 film, Star!, loosely based on her life, Lawrence was portrayed by Julie Andrews.