Her cousin Eliza married a French nobleman who was beheaded during the Revolution, and Eliza barely escaped France with her life. My memory is that she and Jane were close before her marriage but that Jane disapproved of her putting moves on Jane's brother, who was younger than Eliza. This is all residual memory from the Tomalin biography pf Austen that I read over 15 years ago.
I have the 6-volume Oxford edition of Austen. LADY SUSAN is in it, along with the unfinished THE WATSONS and SANDITON and her juvenilia, like her History of England.