Lucy Franklin, director of the District's troubled Historic Preservation Office, has resigned effective Sept. 1, after months of criticism of her performance by federal and local officials.

The National Park Service recently suspended Franklin's office for two months from participating in federal grant programs because of what the federal agency described as "long-standing budgetary and staffing problems."

Also, D.C. Auditor Otis H. Troupe's office began an investigation of the Historic Preservation Office's handling of funds and personnel at the request of City Council member John A. Wilson (D-Ward 2). A draft of that report is expected to be released later this month.

Carol Thompson, director of Licenses, Investigations and Inspections who oversees the historic preservation office, confirmed yesterday that Franklin had submitted a letter of resignation and that a search is under way for a replacement. The office was transferred to Thompson's newly formed super agency from the Department of Housing and Community Development in April.

Asked whether the auditor's investigation and federal criticism of the preservation office were factors in Franklin's planned departure, Thompson replied, "I can't say that was a determining factor, but I'm sure it was a factor."

Franklin could not be reached for comment.

Lawyers and community activists involved in historic preservation reacted positively yesterday to word that Franklin intended to step down.

"A change in leadership was due," said Robert Peck, president of Don't Tear It Down, a Washington preservation group. "I think it's clear there were both managerial and leadership problems in the preservation office."

Ernest Harper, chairman of the city's Joint Committee on Landmarks and a severe critic of the preservation office, said that Franklin's departure "will bode well for the preservation process in Washington. I think Thompson has done a very good job in correcting the problems that have arisen under Miss Franklin's management. "I would commend Miss Franklin for leaving gracefully."

Harper, whose committee had official standing with the city until a recent change in the law, said Franklin's most serious problems included her failure to report to the U.S. Department of the Interior how federal funds were being dispersed and delays in nominating properties to the National Register of Historic Places.

A Washington lawyer who specializes in historic preservation cases said that both preservationists and business executives had been concerned about the problems in the D.C. office.

"There was no real organizational structure in what was occurring," said the lawyer, who asked that his name not be used. "There often were long delays between the time applications were made and public hearings . . . . I don't think she Franklin even understood the process."