A D.C. Superior Court jury this week awarded $225,000 to the mother of a 26-year-old prisoner killed with a hatchet at Lorton Reformatory in April 1980.

The jury deliberated less than two hours before deciding late Wednesday that the city should pay damages to Beatrice Smith Miller, 53, of Kenansville, N.C., for the death of her son, Bradley Smith, who was attacked while asleep in his dormitory.

Smith died 25 days after the attack by two inmates, one wielding a hatchet. He had been serving an 8-to-25-year sentence following a conviction here for second degree murder in 1977. That conviction was under appeal when Smith died, his lawyer said.

Miller filed a $33 million suit against the city shortly after her son's death, claiming that the city had a duty to provide for the safety of her son while he was in Lorton.

Her lawyers, Samuel M. Shapiro and Cassandra P. Hicks, argued that the city had been negligent in failing to protect Smith, in part because prison officials had not taken sufficient steps to find the hatchet used in the attack. They said the hatchet had been missing for eight months inside the institution.

Attorneys for the city argued that Lorton officials had not been negligent and that Smith had been offered, but refused, protective custody following an altercation with several inmates six weeks before his death.

Smith, who was attacked shortly before 6:30 a.m. on April 5, 1980, suffered hatchet wounds on his head, face and back and multiple stab wounds in his stomach. Two inmates later were found guilty of his murder and are serving sentences in maximum security at Lorton, Miller's lawyers said.