Gregory and the others "tried to exit the warehouse, but were unable to exit due to the unsafe conditions and configuration of the warehouse," the lawsuit alleges.
Gregory was one of 36 people killed Dec. 2 when fire broke out in the converted warehouse that was hosting a $10-a-head music performance and party.
It was the deadliest building fire in the United States in more than a decade.
"It's really horrific, irresponsible actions and inactions on the part of this building owner, those associated with this event, and the city that cost the life of this beautiful young lady and the lives of 35 others," lawyer Mary Alexander, who filed the lawsuit on behalf of parents Kimberly and David Gregory, said by phone.
Lawyers retained by the building owner and chief tenant did not immediately return requests for comment Friday.
Gregory's body was found with that of Alex Vega, 22, who had been her boyfriend from high school. Vega's arms were around her, the lawsuit said, citing the coroner's office.
The lawsuit seeks unspecified damages from building owner Chor Ng, principal tenant Derick Ion Almenda and others who lived and used the work spaces and makeshift rooms in the warehouse and promoted the night's event.
The Alameda County district attorney's office has said it is evaluating whether any criminal charges are warranted in the blaze.
Alexander said the family planned to file a separate claim against Oakland alleging negligence by city officials.
People living in and near the building had lodged repeated complaints to building inspectors, police and others about parties, trash and illegal residences at the converted warehouse.