This lady's name was Douglas

 

Not her surname. Her first (given) name was Douglas.

Lady Douglas (or alternatively, Douglass) Sheffield is most widely known as the mother of Robert Dudley, styled Earl of Warwick, the illegitimate son of Robert Dudley, 1st Earl of Leicester, a favorite of Queen Elizabeth I of England.

Some information from Wikipedia:

Douglas is a Scottish and English masculine given name which originated from the surname Douglas. Although today the name is almost exclusively given to boys, it was used as girls name in the 17th and 18th centuries, in the north of England... Linguistically, Douglas is derived from the Gaelic elements: dubh, meaning "dark, black"; and glas, meaning "stream" (also a derivative of glas, meaning "grey").