The Attorney-General warns the onus is now on Bill Shorten to live by the same standard he has demanded of the government when it comes to the dual-citizenship debacle.
Lambie, who first entered the senate in 2013 as a member of Clive Palmer's Palmer United Party, left, and was re-elected as an independent senator previous year.
Tasmanian senator Jacqui Lambie has foreshadowed her possible resignation on Tuesday as she awaits advice from British authorities over whether she is a United Kingdom citizen by descent through her Scottish-born father.
"His father, my grandfather, came to Australia to enlist in the Army in fact", she said in a statement.
The ABC understands Senator Lambie has been telling her colleagues that she may have to join the seven other federal politicians who have departed Parliament House during the citizenship crisis.
Lambie's departure follows the resignations of five fellow senators; the Greens Scott Ludlam and Larissa Waters; the deputy leader of the National party, Fiona Nash; One Nation's Malcolm Roberts; and the Senate president, the Liberal Stephen Parry.
"I didn't think I actually had a problem with it, so I never gave it a second thought " she told Tasmanian radio station LAFM, of her newly-confirmed status.
The resolution requires MPs with dual citizenships to provide details and evidence of the date and manner of renunciation. The deal could see several MPs resign from parliament, forcing by-elections in several seats, and potentially costing the Turnbull government its majority.
When questions were raised over her family history last week, the Senator said: "I'm happy to put on record that I'm satisfied that my parents are both Australian citizens and I have no concerns about me being a dual citizen because of where they were born or came from, in the case of my father, as an infant".
Her replacement in the Senate will be determined by the High Court.
The government and main opposition party cobbled together a deal on Monday to agree to a deadline of December 1 for all politicians to disclose the birthplace of their parents and grandparents.