Joanna Law was one of seven children of Edmund Law, Bishop of Carlisle. She married Sir Thomas Rumbold in May of 1772. Rumbold had amassed a fortune in India, was elected to British Parliament in 1770, and became a baronet of Woodhall in Hertfordshire in 1779. He became the Governor of Madras, India from 1777 until his resignation for ill health in 1780. Thus, like several of her siblings, including Thomas Law, Lady Rumbold likely lived in India during this time. Her brother, Thomas Law, married Elizabeth Parke Custis, Martha Washington’s granddaughter.