His wife and eight workers at the clinic were also charged in the case. Six of the workers have pleaded guilty.
Mongar's estate is being administered by her daughter, Yashoda Devi Gurung. The lawsuit names the city's health department and Health Commissioner Donald Schwarz as defendants.
A spokesman for the health department said he had not yet seen the lawsuit and was unable to comment.
The lawsuit, which was first reported by the web site Courthouse News Service, said Mongar's death could have been prevented had the health department and top officials implemented and enforced policies regarding hazardous and unsafe conditions at the clinic.
The lawsuit noted that a city health worker twice visited the clinic in July 2008 and October 2009 and took note of the "deplorable" conditions - including "bloody fetuses stored in a freezer" - and reported them to her supervisors.
But the lawsuit said the reports were not passed on to higher-ups so steps could be taken to eliminate the hazardous conditions. (A grand jury report in January made similar findings and described the clinic as a "baby charnel house" where Dr. Gosnell performed illegal late-term abortions for poor women.)
Gurung's lawsuit seeks unspecified punitive damages for violations of Mongar's civil rights.