The Nix film shows the bullet hitting the president, First Lady Jackie Kennedy climbing on to the boot of the limousine, and secret service agent Clint Hill jumping into the vehicle.
The film is shot from Dealey Plaza, showing Zapruder across the street and the famous grassy knoll, from where some witnesses thought they heard a shot fired.
It is not as complete as the Zapruder movie, as it shows only part of the assassination.
However, the lawsuit cites the Warren Commission - which investigated the assassination - as saying the Nix film was "nearly as important as the Zapruder film".
The government purchased the Zapruder film for $16m in 1999 in a settlement with his heirs.
Orville Nix sold his film to UPI for $5,000 with an agreement for its return after 25 years.
But it was handed over to the government for the inquiry.
Its last known sighting was with the House Select Committee on Assassinations in 1978.
It was believed to have been handed to the National Archives and Records Administration, but the lawsuit says the agency has told Ms Nix Jackson, who lives in Fort Worth in Texas, it no longer has the movie.
Ms Nix Jackson told the Associated Press it was incomprehensible authorities would lose "an important piece of historical evidence".
She said: "I can understand little clerical issues. I don't understand the loss of evidence like this."