This portrait was painted by Anna Rosina Matthieu &/or Georg David Matthieu. She married twice and is also known as Anna Rosina de Gasc. Georg David Matthieu was her stepson and nephew, since she first married her sister's widower, the painter David Matthieu (1697-1756). Georg David was only 16 at the date given for this painting, so is unlikely to have contributed much, if anything to it.
Johanna Elisabeth of Holstein-Gottorp, was Princess Regent for Friedrich August, Prince of Anhalt-Zerbst (1734-1793) until he came of age in 1752. It's possible that she is the subject of this Portrait of a Lady by Anna Rosina Matthieu, whose appointment as Court Painter to Anhalt-Zerbst was made within three years of the given date of the painting. Johanna Elisabeth was the mother of Catherine the Great of Russia. Her son Friedrich married Princess Caroline Wilhelmina Sophie of Hesse Kassel, who may be the subject of Portrait of a Lady by Tichbein.
The donor, Baroness Maud Ledyard von Kettler, was a railroad heiress whose grandfather was Mayor of Detroit. Her husband, Baron Clemens August Freiherr von Kettler was in the German Diplomatic service in China, first as an Interpreter in Guangjzhou (Canton) later as a top diplomat to Beijing, where the Boxer Rebellion took place. He was assassinated for his part opposing the uprising.
It isn't clear whether he purchased or inherited the painting.