The pay and benefits package, that also included four first- and business-class flights back to New Zealand for her and her husband, made her Britain's best paid public servant.
Under the terms of her contract, made public last year, Dame Lowell must give three months written notice to the Home Secretary. But Amber Rudd, the new Home Secretary, using discretion allowed for contractually, announced Dame Lowell was stepping down with immediate effect. That means she could still be paid for a further three months - equivalent to £90,000 (NZ$164,000).
A Home Office spokesman did not deny that could be the case. "It is reasonable that we allow Dame Lowell time to make alternative living arrangements."
A source said they would continue paying her London accommodation.
Dame Lowell stepped down as inquiry chair in the wake of criticism of her pay deal and the amount of time spent abroad during her first year in charge.
She is the third inquiry chairman to quit following the resignations of Baroness Butler-Sloss and Fiona Woolf.
The Home Office said it was urgently seeking her replacement but Lord Macdonald, the former director of public prosecutions, said the role was now so toxic that it was "not so much a poisoned chalice but a lethal injection".
Lord Macdonald added: "As for finding someone to take this on, this is going to be extraordinarily difficult.
"I can think of many people who would be qualified. I can't think of many, if any, who would be prepared to take it."
Keith Vaz, chairman of the Home Affairs Select Committee, said he planned to call Dame Lowell to give evidence to MPs.
Mr Vaz said: "I think what's really important is that we find out the reasons why she has decided to take this course of action.
"I've written to her today to ask her to come before the committee when we return at the end of August and share with us her thoughts about the setting up of this inquiry and why she resigned, and where she thinks we could go."
Peter Saunders, who sits on the inquiry's Victims and Survivors' Consultative Panel, described Dame Lowell's departure as a "blessing in disguise".
Mr Saunders, a child sex abuse campaigner, said: "This will give us the impetus to get going. We have been frustrated by the slow pace of the inquiry."
Some lawyers have predicted the inquiry, under Dame Lowell's stewardship, could take at least 10 years.