Peers have been debating whether doctors should be allowed to help some terminally-ill people to die.
The late Diane Pretty fought a long court battle for an assisted death
Anglican bishops are among the most fierce opponents of the measure, which is set to be contained in a private member's bill.
Lord Joffe said his bill would make it legal for doctors to prescribe drugs that a terminally-ill person could take to end his or her own life.
He said just having the prescription would take the pressure off patients.
The cross-bench peer previously introduced a bill proposing terminally ill people could choose "medical assistance to die".
That bill proposes enabling "a competent adult who is suffering unbearably as a result of a terminal illness to receive medical assistance to die at his/her own considered and persistent request".
Peers packed the Lords to debate the findings of a select committee report into the bill. The debate ended after midnight on Monday without a vote taking place.
Lord Joffe has said he will introduce a new Assisted Dying for the Terminally Ill Bill after the debate, which would not allow the doctor to directly administer lethal doses of drugs.
Former human rights lawyer Lord Joffe said the measure would "not seek to impose anything on anybody" but would propose another "end of life option".
Lord Joffe, a former chairman of Oxfam, estimated that 650 people a year would use the medication.
'Gift' of life
Anglican and Catholic church leaders have spoken out against voluntary euthanasia.
The Archbishop of Canterbury, Dr Rowan Williams, wrote in the Mail on Sunday that life was "a gift from God that we cannot treat as a possession of our own to keep or throw away".
And in the Lords debate, his predecessor as archbishop, Lord Carey of Clifton said: "Medicalised killing is wrong.
"There are important civil reasons why society as a whole and its more vulnerable members would be threatened if the law were to be changed."
Liberal Democrat MP Evan Harris, a former hospital doctor, said the faith leaders were entitled to their opinions.
But he argued "they should not be seeking to impose their religious views on the rest of the population".
Health minister Lord Warner told peers that the government remained neutral on the issue, but said the bill raised "profound and complex ethical questions".
"There are complex arguments which the government feels it needs to listen to and consider carefully from a position of neutrality," he said.
The British Medical Association dropped its long-held opposition to assisted dying in July, voting at its annual conference to adopt a neutral stance on the issue.
The Voluntary Euthanasia Society said it would be "a little bit disappointed" if voluntary euthanasia was excluded from Lord Joffe's bill.
"We do think there are a lot more people, especially those with a terminal illness, who would prefer to have a choice or prospect that a doctor would help them directly," a society spokesman said.