The Alexandria City Council appointed Vola Lawson, a 14-year city employe, as city manager yesterday, thus endorsing her seven months as the acting chief administrator of a government that has been buffeted by discord.

The council picked Lawson, 50, from more than 50 applicants who had applied for the $75,000-a-year job. She has been the city's acting manager since Feb. 26 when she replaced Douglas Harman, who resigned to become manager of Fort Worth.

Lawson, who will face issues and bitterness stemming from the same controversies that dogged Harman, was given a standing ovation from a crowd of city employes and well-wishers in the Council Chamber as she was voted into office.

Among those present were former mayor Charles E. Beatley, who picked Lawson as Harman's temporary replacement, and Public Safety Director Charles T. Strobel, with whom Lawson has sometimes been at odds.

"She's my girl," said Beatley, fresh from a vacation in England.

Strobel quickly strode from his seat in the gallery to offer his congratulations and pose for a photograph with her. "I look forward to the continuing professional relationship with Mrs. Lawson," he said.

The City Council met secretly last Sunday at an undisclosed location to interview the top six contenders for the administrative post.

Despite what council members described as "tough competition" Lawson apparently became the unanimous choice by the end of that marathon 12-hour session.

"I noticed she talked with such enthusiasm about the city and the role of public service," said Mayor James P. Moran when asked what gave Lawson the edge. "We were all sitting forward in our seats."

Moran, who upset Beatley in the city's spring elections, has been a longtime supporter of Lawson.

Lawson, who took over Harman's job amid strained relations between the council and her office, quickly became popular among council members and was regarded as the front-runner for permanent appointment to the post.

Even so, the council hired Chicago management consultant Paul A. Reume at a cost of $16,000 to gather a list of applicants for the position.

Lawson, known for her quick wit, creativity and take-charge approach, did encounter some resistance from the business community whose leaders wanted a manager with more fiscal experience. Some city employes have expressed reservations about Lawson's reported stubbornness.

"When Vola takes a stand, she's got 20 good reasons why she takes it," council member Del Pepper said yesterday.

A native of Atlanta, Lawson began her government career in 1971 as assistant director of the Alexandria Economic Opportunities Commission. A former city Democratic Central Committee member, she led the 1970 campaign that elected Alexandria's first black council member, Ira L. Robinson.

She helped establish Alexandria's Commission on Women and in 1980 became the city's first housing director. Her tenure there saw the initiation of almost $115 million in low-income and senior citizen housing projects.

Lawson drew praise from the council for recommending that it cut real estate tax assessments by 2 cents and for her quick move to revamp the police department's dispatching system after an incident in which an 89-year-old woman was assaulted.

Lawson has said one of her top priorities will be to deal with low morale in the police department caused by council efforts to trim benefits for officers and a reduction in promotion opportunities due to a reorganization in the department.

In addition, Lawson has said she intends to do an major review of the Public Safety Department to see how its administrative procedures, which have led to public controversies, can be improved.

"I'm deeply appreciative of the confidence the mayor and members of City Council have shown by my appointment as city manager," Lawson said yesterday as her husband David, a clinical psychologist, and her two sons, David, 23, and Peter, 19, listened.

Among the finalists interviewed by the council were Stephen T. Honey, city manager of Portland, Maine, and Thomas D. Dalton, manager of Saginaw, Mich. The other finalists were not identified.