Lilla Burt Cummings, the first woman to serve on the five-member D.C. Board of Zoning Adjustment, resigned yesterday for reasons that neither she nor Mayor Walter E. Washington's office would explain.

Cummings, 47, a lawyer and real estate brier in the District, was named to the board in March, 1973, to fill a vacancy caused by the resignation for health reasons of Howard H. Mackey.

She continued to serve on the board, which decides citizen requested for zoning exceptions, for seven months after Mackey's term expired. Her position became an issue in the 1974 mayoral campaign when mayoral challenger Clifford Alexander criticized Wahington for his failure to place women in top jobs.

Alexander said that at the time that Cummings "did her job so well" and served "citizens' interests" rather than "special interests" to a point that she was an undesirable appointee in Wahington's administration.

A spokesman for the mayor said no comment would be made on Cummings letter of resignation, submitted yesterday, because Washington was out of town.

Cummings said she did not know of the mayor's absence when she delivered the letter and felt it inappropriate under the circumstances" to state her reasons for resigning.