Ordering a payment of lost wages for the first time, the D.C. Board of Labor Relations has told the University of the District of Columbia to rehire a faculty member who was dropped last year when an academic program was reorganized.

In a decision released yesterday, the board said Doris Johnson was entitled to reinstatement as an assistant professor of psychology when a full-time job opened at UDC for which she was qualified.

Under the order, Johnson apparently would be entitled to gross back pay of about $20,000, less any money she has earned on other jobs since she was terminated in September 1977. The board said the figure will be set by a special referee.

Sidney O. Hall, president of the UDC Faculty Association and physical education director at the university, hailed the decision, saying it nailed down the faculty's right to bargain with the university administration on job-related issues. The faculty association is a union affiliated with the National Education Association.

Earlier, the labor board had found a forerunner of UDC, Federal City College, guilty of unfair labor practices when it terminated Johnson and 19 other Faculty members in a way that forcclosed any right to be transferred to other jobs. Federal City College was merged into UDC last year.

As a result of its finding, the board ordered that all 20 be put on a preferential rehiring list. The Johnson case was the first test of that order.

Never before in six years of operation has the labor board ordered the repayment of a lost salary. The law that created the board as the arbiter of disputes involving D.C. government agencies is not explicit in stating the board's power to do so. However, a mayoral order gives the board a broad mandate to prescribe remedies for such disputes.

The payment of back salaries in such cases is not uncommon in private industry.

Martin R.Baach, attorney for Johnson and the faculty association, said Johnson was gratified when told of the order, She could not be reached for comment.

Albert R. Carter Jr., UDC labormanagement specialist, said be had not read the order. "To the extent that there are no technical oversights by the (labor relations) board, we would be obligated to comply," he said.

Johnson was among a group of faculty members hired by Federal City College to teach in a special federally funded extension program called Upward Mobility College. Upward Mobility College was established under contract to protect academic training for employes of the U.S. Department of Health, Education and Welfare.

In 1976, Federal City College decided to switch from full-time to part-time faculty for the Upward Mobility program, and ordered a two-step reduction in force, dropping the 20 affected instructors and professors outright.

The faculty association insisted the cutack should be negotiated. The labor board upheld the association, and ordered that the 20 be given preference in reinstatement to other college job as vacancies occured. UDC at one point insisted that Johnson's status on the Upward Mobility program did not qualify her for the regular faculty, but the board ruled that it did.