The Barry administration removed the No. 2 official of the troubled D.C. Department of Labor yesterday and will replace him with a former member of the city school board.

A high-ranking city offical disclosed that Lorenzo M. White, the department's acting deputy director, will be succeeded on Monday by Mattie G. Taylor, a middle-level department official who served on the school board from 1969 to 1974. White will be reassigned in the department without loss of civil service rank, the official said.

The departmenths top official, acting director Thomas A. Wilkins, was removed by Mayor Marion Barry in mid-February and transferred to a federal government job. White, who was wilkins' deputy, was regauded as the department's chief administrator.

Taylor has served recently as director of Manpower Outreach for the department's employment service. Apart from two assistant city administrators, Taylor's appointment is the highest to go to a woman since Barry took office Jan. 2.

For part of the time Taylor served on the school board, Barry was the board's predident. She was then one of his chief critics.

The D.C. Coalition for Women's Appointments recommended last year to then-mayor Walter E. Washington that Taylor be considered to replace Wilkins in the top job. Washington did not act on that suggestion.

The D.C. Labor Department was created last year when the city's manpower agency was reorganized.The result was that all the department's top officials hold their jobs on an acting basis. The current acting director is Matthew F. Shannon, who also serves as a special assistant to Barry.

The department had been strongly critized for ineffective delivery of services and for cronyism and favoritism among its top officials.