Businesswoman Mellody Hobson and her husband, filmmaker George Lucas, are seeking to take control of Ebony and Jet magazines’ archives, a collection of thousands of pictures and recordings chronicling about 70 years of African-American life and culture that includes original photos of Martin Luther King Jr., Rosa Parks, Muhammad Ali and Maya Angelou.

The archives are currently uninsured and their continuing preservation has been put at risk because of the recent bankruptcy of the magazine’s former owner, Johnson Publishing...