During the 1760s and 1780s Robert and James Adam were commissioned by Sir James Lowther, Baronet (created 1st Earl of Lonsdale in 1784) (1736-1802) to make designs for Lowther Hall and Whitehaven Castle, both in Cumberland. Doubtless this fire screen for 'Miss Lowther' can be attributed to the patronage of Sir James Lowther, but not necessarily for either of these houses. It is significant to note that 'Miss Lowther' is unknown.
In 1755 Sir James married Lady Mary Stuart (1740-1824). The marriage was an unhappy one, and they had no children: Sir James had no daughter with Lady Mary called 'Miss Lowther'. It is possible that she was a female relative of Sir James's, or even an illegitimate daughter by one of his many mistresses, but this is not known, and it is not possible to say whether any such lady resided with him at Lowther Hall or Whitehaven Castle.
See also: Lowther Hall and Whitehaven Castle
Literature: 'Lowther, James, Earl of Lonsdale (1736-1802)', Oxford dictionary of national biography online