Attorneys for Palms' family claim the store's security measures were outdated and that store personnel could have prevented the shooting.
Robertson was allowed "to enter into a private employee security entrance and then follow Tranesha Rashon Palms into a restricted employee area where he then shot and killed her," the suit alleges.
The suit also claims that store management ignored threats made by Robertson just days before the shooting.
"Employees of the Old Navy knew that he was following her, saw that he was following her, knew that she didn't know that he was behind her, and didn't warn her," said attorney Cannon Lambert.
The family is asking for at least $50,000 in damages. A spokeswoman from Gap Inc., Old Navy's corporate parent, said the company hasn't seen a copy of the lawsuit, but said safety and security of employees and customers is of the "utmost importance."
Palms and Robertson were romantically involved and had a 2-year-old son, but neighbors said they'd heard the couple fighting multiples times over the course of the previous year.