Elizabeth was the daughter of the redoubtable Bess of Hardwick by her second husband Sir William Cavendish. In 1574 she was secretly married to Charles Stuart, 1st Earl of Lennox, the younger brother of Henry Stuart, Lord Darnley, and thus a claimant to the English throne. Both sets of parents incurred the wrath of Queen Elizabeth I for having arranged such a controversial marriage without her permission, and Elizabeth's mother-in-law, Margaret Douglas, was sent to the Tower of London.
The following year, Elizabeth gave birth to her only child, Arbella Stuart. Her husband died in 1577.