The U.S. Attorney's office has launched a grand jury investigation to determine how a 39-year-old Washington woman, convicted yesterday of murdering one adopted child and beating two others adopted a fourth child while awaiting trial on the murder charge.

A D.C. Superior Court jury yesterday convicted Lillie Mae Caldwell Gasaway of Northwest Washington of second-degree murder in the September 1979 beating death of a 9-month-old adopted boy, Hildred Thomas Gasaway, and two counts of cruelty involving assaults on two other adopted children -- Varatia, 7, and Nathan, 2. All three children had been punched in the stomach, according to court testimony.

Judge Fred B. Ugast, who presided over the two-week trial, disclosed after the verdict was announced yesterday that he had learned about the fourth child in a private conference at the bench with defense attorney Carrie Fair.

The fourth child has since been taken away from Gasaway. The two-year-old was taken from her in 1978 and the 7-year-old shortly after gasaway was charged in 1979.

The circumstances under which Gasaway adopted the children prompted Ugast to make an unusual appeal from the bench for improved regulations affecting adoptions in the city.

Gasaway applied to adopt Hildred three years before the adoption was granted, according to Assistant U.S. Attorney Richard L. Caplan, who prosecuted the case, but the agency granted the adoption without determining whether the original information was still valid.

Gasaway adopted Varatia from the Lutheran Social Services agency in 1974. Sometime after that, she adopted a second infant from the same agency, but returned it after a short time.

In August 1978, she obtained Nathan from the same agency. A month later, she applied for welfare benefits from the city and began receiving about $300 a month for the two children, Caplan said.

At the time, Gasaway claimed she was unemployed, Caplan said, but was actually working at the Walter Reed Army Medical Center, earning $10,000 a year.A child-abuse investigation was launched when, during her welfare application interview, Gasaway disclosed that she had tried to kill Varatia.

The Child Protective Services division of the D.C. Department of Human Services subsequently made monthly visits to her home, and in January 1979, she obtained Hildred from the Family and Child Services agency of Washington, D.C. The child was dead nine months later.

Caplan said private adoption agencies generally do not check the backgrounds of prospective mothers with city social workers. He also said they do not make it a practice to determine if the prospective mothers have criminal records.

D.C. police on two occasions investigated child abuse allegations involving Gasaway, Caplan said, but concluded each time that the claims were unsubstantiated.

Police interviewed Gasaway in the spring of 1979 after one of her adopted children, Nathan, was treated at Children's Hospital for a fractured skull. The officers accepted the mother's explanation that the child hurt his head when he fell against a table, Caplan said.

At the same time, city social workers were investigating complaints of child abuse involving Gasaway, but police were unaware of that. Had the police known of the social workers' probe, they would not have dropped their own investigation, Caplan said.

"The problem is there's no communication betwwen police and child protective services," Caplan said. "They don't talk to each other about their cases."

Caplan also said that the city should provide stronger safeguards against the submission of false information on adoption applications.

He said Gasaway told one adoption agency that Varatia was her natural daughter rather than an adopted one, said she was single when she was actually married, and she said she was six years younger than she actually was.

During the trial, a doctor from Children's Hospital testified that Nathan suffered from maternal deprivation and failed to gain any height or weight during the year he spent with Gasaway -- an unusual situation for a child of that age.

During the trial last week, Gasaway was formally charged with trying to run over a key government witness in the case.