The "Christian Dior: Designer Of Dreams" fashion exhibition will also feature outfits worn by Princess Margaret and the Queen Mother.
The late Princess' 21st birthday Dior gown, which was embroidered with straw-raffia, is expected to be one of the top draws at the Victoria & Albert Museum showcase, alongside Lawrence's dress, on loan from the Dior heritage archive. and items worn by celebrated ballerina Margot Fonteyn.
The new Dior exhibition is expected to be the museum's biggest since curators staged a tribute to Alexander McQueen in 2015.
The exhibition, which is slated to begin in February (19), will also chronicle the private fashion shows Dior staged in London for Princess Margaret and the Queen Mother in the 1940s, and study the legacy of the beloved French designer.
More than 200 dresses, all made by hand, will be on display, alongside accessories, cosmetics and photography.
Oriole Cullen, the fashion and textiles curator at the Victoria & Albert Museum, insists Christian Dior is so beloved because he helped to change the face of fashion, while redefining "the female silhouette" and reinvigorating "the post-war Parisian fashion industry."
"Christian Dior: Designer Of Dreams" will run from February 2 to July 14 at the London museum.
Meanwhile, Oscar winner Lawrence, who has been a spokesmodel for Dior since 2013, was recently unveiled as the face of the fashion house's latest campaign - the 28 year old's second for Dior in as many months. She also served as the face of Dior's scent Joy last month and appeared in a short video, directed by Jean-Baptiste Mondino, as part of its promotion.
Jennifer previously headlined a handbag campaign in 2013, as well as ads for Dior Addict Lipstick in 2015.