"As program director at the time, I am ashamed that this happened on my watch and I take full responsibility," Lawrence said in a statement on Monday.
She added that increasing concerns over the behavior of staff in Chad and Haiti in recent days showed "that we failed adequately to act upon."
She added that the sexual misconduct allegations were first raised against some Oxfam staff in an earlier mission in Chad.
"It is now clear that these allegations - involving the use of prostitutes and which related to behavior of both the Country Director and members of his team in Chad - were raised before he moved to Haiti," Lawrence said.
The charity group has apologized unreservedly for misconduct allegations against staff members in Haiti but emphasized that it has no intention to cover up the scandal.
The sexual misconduct allegations were leveled against Roland van Hauwermeiren, who was Oxfam's country director for Haiti and was previously the head of the charity's mission in Chad.
The group investigated the allegations in 2011 and van Hauwermeiren was one of three staff members who resigned while four others were dismissed.
At a meeting earlier on Monday with International Development Secretary Penny Mordaunt, Oxfam's chair of trustees Caroline Thomson and chief executive Mark Goldring had been called to explain themselves.
Mordaunt warned on Saturday that all charities that receive Britain's funding to tackle sexual wrongdoing among staff or face having their aid cut.
Oxfam, which employs around 5,000 staff and has 23,000 more volunteers, received 43.8 million dollars (31.7 million pounds) from the government in the last financial year.
Goldring said Saturday that Oxfam receives less than 10 percent of its funding from the UK government and hoped to continue working with Downing Street while rebuilding trust with the public.
Oxfam is also accused of failing to warn other aid agencies about the staff involved, which allowed them to get jobs among vulnerable people in other disaster areas.
Nearly one in five people working in Britain’s Parliament were also sexually harassed or witnessed inappropriate behavior in the past year, said a report commissioned after a series of sex scandals at Westminster.
The report, published on Thursday, called for a new complaints procedure along with radical change of a culture that can deter some from challenging bosses and suggested forms of punishment for those found guilty of harassing their staff.
The British Labor Party in November suspended a parliamentarian and a former minister over accusations of sexual harassment, further deepening the Westminster sex abuse scandal.
The party made the decision about Ivan Lewis and launched an investigation into allegations of sexual harassment leveled against the MP.