"This is very distressing for all the family, a decent family. And it got worse with the news (from Kenya). It's also very distressing for the people of Banbridge, on behalf of the family," she said.
According to the Belfast Telegraph, Lewthwaite's father was a British soldier posted to the area who married a local woman.
Kenyan officials have given differing accounts of the involvement of a white woman in the Westgate Mall attack.
Senior Kenyan intelligence officials told CNN that surveillance video from inside the mall appeared to show such a woman taking part in the attack. Analysts believe she is British, the sources said.
Kenyan Foreign Minister Amina Mohamed told "PBS NewsHour" on Monday that a British woman was among the attackers. "She has, I think, done this many times before," she said of the woman but did not name the suspect.
Kenyan State House spokesman Manoah Esipisu told CNN that "multiple witnesses" have said they saw a woman among the attackers.
"We have also been told that if it is the same woman that they say they saw, that she would have been killed very early on in the attack," he said.
But he cautioned, "We don't know for sure that we had a woman. And secondly, because of the bodies trapped under the rubble, we don't know if she is who everyone says she might be."
Kenyan Interior Minister Joseph Ole Lenku previously told reporters that all the attackers were men. Some of them apparently had dressed as women, he said.
But on Wednesday, he revisited the speculation that a woman was involved, saying that authorities were "hearing possibilities and information," including from the public. "We want to again request you to allow the forensic experts to determine whether that is true," he said.
Female involvement in such an attack would be "very unusual," said CNN security analyst Peter Bergen.
"Typically these groups are misogynist," he said. "Their view is the woman should be in a home and shrouded in a body veil."