The Justice Department sued the financially troubled Lacaze-Gardner School yesterday, seeking to recover more than $1 million in tuition money paid by students and the federal government to the now-defunct Washington branch of the school.

The school, which offered secretarial, typing, keypunch and business management courses to 900 students -- most of them low-income -- "will be unjustly enriched" if permitted to retain tuition money for the period after Nov. 10, 1978, when its downtown Washington branch closed, the government said.

A Justice Department official estimated that the school has "substantially in excess of a million dollars" in government funds that were advanced to it under a variety of student-aid programs. The shcool also is holding an unknow, but probably lesser amount of students' money that the government suit seeks to recover for them.

Lacaze-Gardner is under investigation by the U.S. Office of Education and the FBI for allegedly abusing federal student financial aid programs by obtaining millions of dollars for tuition for students who failed to complete courses there.

The school announced Nov. 8 that its downtown branch, at 710 14th St. NW, was closing and would accept no future students. The next day, two fires, caused by arson according to fire officials, broke out in the school. On Nov. 13, the D.C. fire marshal formally ordered the school to close. Branches of the school in Langley Park and Falls Church are not affected by the order to close and are still in business.

According to the government's suit, federal funds were advanced to Lacaze-Gardner in June 1978, under contracts signed by the government and the school.

Despite the closing of the Washington branch, the suit charges, Lacaze-Gardner still has "funds which were entrusted to them to use solely for instructional purposes, but which will not be spent for such purposes inasmuch as the... schools are no longer operating."

The suit also takes the unusual step of asking Judge John Lewis Smith, to whom the suit was assigned, to create a trust from the tuition funds owed by the school to its students "and to have the United States appointed trustee for these students to determine the amount "owed to them, and recover and refund these tuition funds to them."

At least six former Lacaze-Gardner students have filed formal complaints with the D.C. Office of Consumer Protection charging that they were deceived in various ways when they signed up for financial aid to attend the school.

One former employe of the school, James Butler Jr., told The Washington Post in November that he falsified test scores and personal financial information so that students could get federal aid. A spokesman for the school declined to comment at the time on Butler's charges.