Twenty-two-year-old Tranesha Palms was shot to death May 7. Police say 27-year-old Eugene Robertson killed her, then himself.
Palms family says four days before the shooting Robertson called and made threats to store managers.
The lawsuit alleges Robertson entered the store through a private employee entrance and wasn't prevented from going into a part of the store that is off limits to non-employees.
"I thought she would be safe at work," said Monique Lowe, Palms's mother. "When we all go to work, we think we're safe, we don't think anything like this would happen at work."
ABC 7 put a call into Old Navy's corporate headquarters but so far has not received a comment about the lawsuit.