A similar bill to legalise assisted dying did not make it through the Lords in 2014 - although unlike Leadbeater's draft law, it had not already been approved by MPs.
Leadbeater said she was "concerned" about the Lords potentially trying to block a bill after the Commons had already "voted to change the law".
Adding that "now is the time" to update the law, she said: "the Lords have to respect that, and we have to respect democracy".
Legalisation of assisted dying did not feature in the manifestos of any of the major parties prior to last year's general election, and parties have agreed to treat it as a matter of conscience, meaning they will not tell their MPs how to vote.
During the earlier debate, before Leadbeater's intervention, former DUP leader Baron Dodds of Duncairn said the bill needed further changes to ensure "all the necessary safeguards" were in place.
He added that the Lords would not need to spend so much time on the bill "had some of these issues been dealt with in a different way" by MPs.
Former High Court judge Elizabeth Butler-Sloss expressed a similar sentiment, telling peers: "There are many of us who do not like the bill, but there is a real probability that the bill will pass, and if it passes, we want it better than it is at the moment. Consequently, we are not wasting time."
Lord Goodman, a Conservative peer who has put forward a number of amendments to the bill, said it had been passed by the Commons "without any of the necessary detail" on how it could be implemented.
Professional groups, he said, had criticised the "shocking state" of the legislation and called for peers to offer scrutiny and amendments.
"Protecting vulnerable people from dying against their wishes, preventing abuse and stopping an enormous burden on the NHS are hugely important goals that we would imagine all would share" he said.
Ministers have ruled out using government debating time to enable further discussion of the amendments in the Lords, but have hinted they are prepared to explore other routes to make more time available.
According to the Hansard Society, a think tank, such options include additional sittings on Fridays, a time traditionally reserved to debate bills put forward by backbench MPs.
Other alternatives include using time that would normally be reserved for other subjects, or sitting for longer hours between Monday and Thursday, it added.