MPs have fast-tracked legislation to compensate victims of historical institutional abuse.
The Historical Institutional Abuse (Northern Ireland) Bill was approved in the Commons having previously been supported by Lords.
Secretary of State Julian Smith urged victims to come forward to make a claim and said around 5,000 people could be eligible for compensation through the redress scheme the new law would set up.
Mr Lewis said: "No matter what country they live in, I would now urge all victims and survivors to apply.
"Whether you are part of a victim's group or whether you have lived with your abuse silently for years, please make use of this redress scheme from this Bill."
The Bill establishes a Historical Institutional Abuse Redress Board to administer a publicly funded compensation scheme for victims in Northern Ireland and also allows for a commissioner for survivors of institutional childhood abuse to be appointed.
Mr Smith said: "It is the first Bill of its kind in the United Kingdom with the results of inquiries in England and Wales and Scotland yet to be completed.
"I hope that this Bill will give some comfort and hope to victims of child abuse from across our country."
Mr Smith welcomed the consensus from the six main political parties in Northern Ireland, and across the Commons, to fast-track the legislation before Parliament is dissolved for the General Election.
He also paid tribute to Sir Anthony Hart, who chaired the Historical Institutional Abuse Inquiry in Northern Ireland, and died in July before his report's recommendations could be implemented.
Mr Smith said: "I know that Sir Anthony was, I think, perplexed by the slowness of all of us to get this done."
Shadow Northern Ireland minister Stephen Pound said: "We cannot make it right, we cannot repair those broken hearts, those broken bodies, but by doing what we will today, by offering some form of redress, some form of compensation, we will hopefully allow closure."
The DUP's Emma Little-Pengelly said she is "angry" that it has taken so long for victims and survivors to get the redress that they deserve.
Ms Little-Pengelly (Belfast South) said: "I think it is such a good thing that we end this Parliament on this type of issue, where the very many hundreds and thousands of those who suffered appalling abuse, which the secretary of state has outlined, finally get the last piece of this process which is redress.
"But can I also highlight that redress won't be closure. Redress will never undo the dreadful wrongs that happened to all of those children in those settings."
Fellow DUP MP Ian Paisley asked for assurances from Mr Smith that the British government will continue to support victims and survivors of abuse.
Mr Paisley (North Antrim) said: "Today is a very, if I can use the word appropriately, it is a very exciting day in that they've now achieved this. But there will then be the cliff edge - well what next?
"Victims groups will have to be wrapped with compassion and charity and help and assistance so that they can then move to the next stage of this.
"Because this is not going to end very quickly. There's probably going to now be a process put in place and it's important that help is given, practical help is given to take those groups through that, and to make sure that they can get to the other end of this as quickly and as expeditiously as possible."
Speaking at the Bill's third reading, Mr Smith said the British government hopes claims will start being considered as soon as the Bill becomes law.
He said: "The government will do whatever it can to make sure we play our part in moving things forward as quickly as possible."
