In the short story The Strange Case of Sir Arthur Carmichael, Lady Carmichael was the stepmother of Sir Arthur Carmichael. She was the second wife of his late father. She dealt in the supernatural. Somehow she switched souls between her stepson and her cat, to prevent him from getting married. With the cat's soul in Arthur's body, he would look insane to the world, and she would control his estate, which would then be passed on to her own son. She killed the cat with Arthur's soul afterwards. She died of a heart attack.
In the Agatha Christie canon there are actually two Lady Carmichaels but their backstories are wholly different.