A biographical article for her, if she is Elizabeth Dalrymple, née Roxburgh, is here. She was born in Philadelphia, Pennsylvania and "It was said that before Elizabeth married Lord Dalrymple, she had been engaged briefly to another English gentleman during the Revolutionary War. Tragically, he was shot by accident in a hunting incident on the estate of the Marquis of Townsend. After his death, Elizabeth attempted to return by sea voyage to America. It was on the voyage home to America, that her vessel was captured, and she was returned to England-- where she met Lord Dalrymple.”
From artuk.org. Also posted to the Revolutionary, Napoléonic, and Romantic Era Album here.