This 1793–94 portrait by Adélaïde Labille-Guiard is presumed to be of the Marquise de La Fayette. It hangs in the National Museum of Women in the Arts in Washington, DC.
The youngest of eight children born to a Parisian haberdasher and his wife, Labile-Guiard earned early praise for her skillfully rendered portraits. She worked for many royal and aristocratic patrons, won admission to France's Royal Academy, and was ultimately awarded a government pension and an apartment at the Louvre. This portrait demonstrates Labille-Guiard's ability to use a minimal number of elements to their strongest effect. Absent are elaborate architectural backgrounds. The sitter wears a simple gown and modest jewelry, a style favored during the early years of the French Revolution. -- NMWA
On May 31, 1783, Adélaïde Labille-Guiard and Élisabeth Louise Vigée-LeBrun became the 12th and 13th women ever granted full membership in the French Royal Academy, bringing the number of female members to its limit of four.
In her earlier portraits of French nobility, Adélaïde Labille-Guiard had proven herself adept at rendering intricate details of elaborate clothing, furniture, and architecture. In Portrait of a Woman (Presumed Portrait of the Marquise de Lafayette), however, the artist created an effective image with minimal elements and ornamentation.
Labille-Guiard’s sitter wears a simple dress of the type favored by women during the early years of the French Revolution. She wears no ornate jewelry. She is not posed in an elaborate architectural setting, and even the landscape backdrop is relatively restrained. Her somewhat tentative smile emphasizes the sitter’s physical attractiveness without unduly flattering her. -- NMWA
Wikipedia has this short biography of Marie Adrienne Françoise de Noailles, Marquise de La Fayette.
Marie Adrienne Françoise de Noailles, Marquise de La Fayette (2 November 1759 – 24 December 1807), was a French marchioness. She was the daughter of Jean de Noailles and Henriette Anne Louise d'Aguesseau, and married Gilbert du Motier, Marquis de Lafayette.They had four children: Henriette (15 December 1775 – 3 October 1777), Anastasie Louise Pauline du Motier (1 July 1777 – 24 February 1863), Georges Washington Louis Gilbert du Motier, (24 December 1779 – 29 November 1849), and Marie Antoinette Virginie du Motier (17 September 1782 – 23 July 1849) She was a great-granddaughter of Françoise Charlotte d'Aubigné, niece of Madame de Maintenon.In 1795, the Marquise Lafayette was imprisoned and about to be executed. Intervention by Elizabeth Monroe saved her. Mrs. Monroe visited the imprisoned marquise on the day before the execution and loudly announced she would come the next day. Not wanting to cut ties with the (then) diplomat (James Monroe), France did not execute her. -- Wikipedia
They include this Portrait Of Marie Adrienne Francoise De Noailles, Marquise De La Fayette (1759-1807) which sold at Christies in 2010 for €18,750.
Portrait Of Marie Adrienne Francoise De Noailles, Marquise De La Fayette
The British Museum has this artist's proof of an 1894 etching of Adrienne de La Fayette by Albert Rosenthal with a “remarque of a portrait of Lafayette” in the lower margin.
This picture also appears in a WWI era article entitled "The Girl He Left Behind Him" by Lida Rose M'Cabe.
This Print is from the Plate Owned by the Marquis de Lasteyrie.