An unemployed engineer killed a 23-year-old woman systems analyst with whom he had once worked and then fatally shot himself yesterday in a startling and unexplained incident that followed a tranquil lunch at a McLean shopping center.

The two, who had been acquainted for a year or more, had "smiled a lot" and "appeared to be happy" as they ate lunch at a restaurant in the Commons Shopping Center shortly before the 12:45 p.m. shootings, a witness said.

Both the man, Christopher J. Thomas, 42, of Falls Church, and the woman, Lucy A. Pirtle, who lived in the District, had formerly worked in an office in the Tysons Corner area for a division of TRW Inc.

Pirtle's most recent supervisor described her as a "young, vivacious, very talented" woman of "tremendous potential." A mutual friend described both her and Thomas as "very nice, very kind and gentle."

Asked last night to provide a motive for the incident in the small shopping center several blocks south of Rte. 123, a Fairfax County police spokesman said: "We don't know."

The two had lunched at The Apple-Tree Deli in the shopping center at Anderson Road and Colshire Drive. A waitress there told a reporter, "If you had asked me the nicest couple I've been in contact with today, I'd say they were.

"They did not appear unusual in any manner," recalled waitress Deborah Irwin. "They were not too quiet. They were not too loud."

She said no argument or disagreement was apparent. "There did not appear to be any tension."

After lunch they were reportedly seen walking in the shopping center parking lot, holding hands, according to Ronald Cain, owner of Cain Security Systems Inc., which has offices in the center.

Cain said one of his employes told him that the mood seemed to change abruptly as the couple approached the woman's parked car.

There, Cain said, he was told by his employe that the woman "pulled away" from the man "as though she was irritated."

Other witnesses reportedly told workers in a dry-cleaning shop that the man opened the car door and the woman screamed.

Then, according to the account, the man shot the woman and then fired at his own head.

The couple collapsed beside Pirtle's car. They were pronounced dead there shortly afterward, Pirtle of a wound to the back of her head.

Police described the weapon used as a handgun.

"It's really a loss," said Pam Moritz, a friend and former coworker of both Thomas and Pirtle.

Thomas, she said, "was really a very gentle, kind, sensitive person." The shooting, she added, "was not in his character at all."

Friends and associates reached last night said that while Thomas and Pirtle had known each other for some time, they were not romantically involved and were not believed to have met many times since both left TRW.

Pirtle, a graduate of Bucknell University and the daughter of an artist who lives in Bethesda, left some time in the spring of 1981 and began working that summer for Simcon Inc., also in the Tysons Corner area.

Thomas, a native of Ceylon, now Sri Lanka, who had lived for many years in the United States, left TRW in February, according to Moritz.

"I hadn't known of them seeing each other much," Moritz said. The times they did meet, she said, were probably at lunches or parties attended by large groups.

"It wasn't a romantic relationship," said a woman at the house Pirtle shared in Northwest Washington with several other persons.

"They knew each other," the woman said, but added that Pirtle's connection with Thomas, believed to hold a PhD degree in mechanical engineering, "seemed more a professional relationship."

Neither was reported to have brought up the name of the other in conversation. In particular, Moritz said, Thomas had said nothing about Pirtle when Moritz last saw him two weeks ago. But she said, they were in a group, and "he was quiet about his personal life."