Revealing her British citizenship through her Scottish-born father, Ms Lambie told the Senate on Tuesday she had "worked hard to be a voice for those who don't often get much of a voice in this chamber" and said she intended to return to federal politics.

"Politicians on both sides of the house talk about helping those on welfare without having had to choose between spending your welfare payment on either school uniforms [or] school lunches," Ms Lambie said in a tearful farewell address, in which she proclaimed her pride at opposing "savage" welfare cuts.

"Unlike some in this place, who say they are there for the battler, I actually refused to deliver the budget into surplus by driving struggling families into further poverty."

The outgoing Tasmanian senator drew warm praise from Labor, Coalition and crossbench colleagues, who lined up to embrace her after her speech.

Attorney-General George Brandis said the high-profile crossbencher had made the Senate a richer place and Labor frontbencher Doug Cameron called for "less lawyers, more Lambies" in federal politics.

"We have all benefited from your company, your wisdom, your life experience and, in particular, from the passion. Passion is a word that is used too freely, too loosely, in politics," Senator Brandis said.

"You have become one of the best-known and one of the best-liked people in this country since you joined the Senate, and the Senate is a better place, a much richer place, for your having served among us."

Senator Cameron said "no one was ever bored" when Ms Lambie was speaking in the Senate and praised her departure from the Palmer United Party six months after entering Parliament in 2013 as "one of the first good decisions you made".

"I think you are a tough, uncompromising, working-class woman and we need more like you in here. Less lawyers, more Lambies, I think," he said.

The British government confirmed to Ms Lambie on Tuesday morning that she had inherited citizenship from her paternal grandfather. In an emotional account, she said her Scotland-born father had mistakenly believed his father had renounced his citizenship.

The man set to take Ms Lambie's place, Jacqui Lambie Network candidate Steve Martin, said being Mayor of Devonport was his full-time job but he was not concerned about a possible breach of a section 44 (iv) of the constitution, which forbids a candidate from holding an office of profit under the Crown.

Mr Martin and Ms Lambie said they had checked his eligibility with Rosemary Laing, the former Clerk of the Senate, and had been told he was in the clear.

"I think I'm fine to stand," Mr Martin told Fairfax Media.

But constitutional law professor Anne Twomey said: "the answer is we don't know, there is an argument that it is not an office of profit as you are elected, not appointed".

"But it is probably an office of profit to the extent you receive remuneration ... The key question is whether it is under the Crown. The relevant factors are, how they are appointed, how they are removed, and whether there is accountability to the [Tasmanian] state government."

If Mr Martin was unable to sit, his spot would likely flow through to the third candidate, Robert Waterman.

Amid calls to amend the constitution and allow dual citizens to sit in Parliament, Ms Lambie said politicians should just "suck it up", deal with their mistakes and then run for Parliament again.

And, she said, she would "never" ask Mr Martin to step aside and allow her to return.

"That spot is his," she said, adding that she would consider contesting the electorate of Braddon should sitting Labor MP Justine Keay be forced out of Parliament by her own citizenship woes.

"I'd certainly have a good look at it ... you can't keep a bloody Lambie down," she said.

The government and Labor have agreed on a disclosure measure aimed at resolving the citizenship fiasco. It will compel all MPs to disclose the details of their birth, heritage of their parents and grandparents, and evidence that any second citizenship was properly renounced.