Dame Lowell, 67, who was appointed in April 2015, had spent more than 70 days working abroad or on holiday during her time in charge.
An inquiry spokesman said she had spent 44 days in New Zealand and Australia on inquiry business and was entitled to 30 days' annual leave.
Campaign groups and politicians have called for a replacement to be found "urgently".
The independent inquiry is looking into potential child sex abuse committed within thirteen British institutions including the Anglican and Roman Catholic churches.
Dame Lowell is the third chairman of the inquiry to step down.
Baroness Butler-Sloss (below) stood down in July 2014 amid questions over the role played by her late brother, Lord Havers, who was attorney general in the 1980s.
Her replacement Dame Fiona Woolf resigned following a barrage of criticism over her "establishment links", most notably in relation to former home secretary Leon Brittan, who died in 2015.
Dame Lowell said: "The conduct of any public inquiry is not an easy task, let alone one of the magnitude of this.
"Compounding the many difficulties was its legacy of failure which has been very hard to shake off and, with hindsight, it would have been better to have started completely afresh.
"While it has been a struggle in many respects, I am confident there have been achievements and some very real gains for victims and survivors of institutional child sexual abuse in getting their voices heard.
"I have nothing but the greatest of respect for the victims and survivors, and have particularly enjoyed working with the Victims and Survivors Consultative Panel which I established."
Revd Graham Sawyer from St James Briercliffe Church in Burnley, who was abused by the former-bishop of Lewes Peter Ball during the 1970s, told Premier Christian Radio he believed human rights campaigner Peter Tatchell was best-placed to lead the inquiry.
He said: "He would leave so unturned and if the government is really serious about getting to the root of all of this and getting the truth out then Peter Tatchell is probably one of the very best people who could be appointed to do that job.
Revd Sawyer went on to say it was important the government must act quickly and consult experts when choosing a replacement, adding: "This needs to be got on with and it needs to be got on with very quickly, not only for the sake of all the victims and survivors but also to try to ensure as few abuse cases occur in the future as possible.
"I hope this time they really do consult very fully with all the people in the safeguarding world to ensure that the new person chairing this inquiry will have confidence."
