The suit, representing 80 families, was filed Wednesday in the U.S. District Court for the District of Arizona. The flight school, Airline Training Center Arizona, did not immediately respond to CNN's request for comment.
Germanwings Flight 9525, headed from Barcelona, Spain, to Dusseldorf, Germany, smashed into a mountainside in a remote area of the French Alps in March 2015, killing all 150 people on board.
The flight's data recorder showed that Lubitz crashed the plane intentionally after locking the pilot out of the cockpit.
The 27-year-old had a history of severe depression, a French prosecutor said.
"If you have a young man, a pilot who was mentally unstable and untrustworthy ... you cannot allow a person to become a pilot with those conditions and put the passengers at risk," said Marc S. Moller, a New York-based attorney for the families.
"The crux is that ATCA, the defendant, is that they had an obligation before they allowed Lubitz into the program to look into his mental history. And had they done that, they would have seen his mental problems and lying."
What the families claim
According to the suit, the flight school required Lubitz to present both German and Federal Aviation Administration medical certificates.
"The notation was printed on the German medical certificate to indicate that his medical certificate would become invalid if there was a relapse or recurrence of his depression," the lawsuit states.
"ATCA knew, should have known, or could have determined that Lubitz ... had an extensively documented history of dangerous and debilitating psychotic and depressive conditions, including reactive depression, (and) that his treatment for those disorders included doctor-prescribed medication that prevented Lubitz from pilot training."
Among the issues: Lubitz suspended his course work for almost 10 months because of his severe depressive disorder, the suit claims. And during that time, "Lubitz was hospitalized and underwent nine months of extensive and intensive psychotherapy for severe depressive episodes, anxiety and suicidal ideations."
The suit does not specify an exact amount the families are seeking, but says they are asking for compensation that a jury "determines is just, full and fair."
A terrifying 11 minutes
During Flight 9525's fatal descent, French air traffic controllers called the flight crew 11 times on three different frequencies without any response. The French military defense system also tried three times to contact the aircraft, without any answer.
The plane's 34-year-old captain had left the cockpit after the plane reached its cruising altitude of 38,000 feet and buzzed to re-enter about four minutes later.
The cockpit voice recorder picked up what sounds like knocking on the door and the sound of a muffled voice asking for the door to be opened.
The captain starts screaming and pounds on the door, to no avail.
"During this sequence of events until the moment of impact, the passengers experienced extreme fear of impending death, panic, pain, suffering and unimaginable mental anguish," the lawsuit states.
It said the entire descent took 11 minutes.