In the interview, Ms Lambie said: "If you are not going to show your allegiance to our law, then get out."
She was left tongue-tied when asked about sharia. "Well I think ... when it comes to ... sharia law ... you know to me ... it obviously involves terrorism. It involves a power that is not a healthy power."
In comments likely to inflame current tensions with the Islamic community in Australia, she suggested even moderate Muslims should abandon their faith because of sharia.
But she said she had no problems with Muslims. "I have a problem with extremists and sharia law," she said.
"I want to see their full allegiance - not 50 per cent to the Australian constitution and Australian law.
"It is one law for all - that is the Australian law, full stop."
A number of Australian Muslims have complained of being targeted following last week's terror raids, with women abused in the street and one having coffee thrown in her face while stopped at traffic lights in Brisbane.
Prime Minister Tony Abbott has called for tolerance towards Australian Muslims, who he has described as "absolutely first-class Australians".
But his stance has not been helped by some in his own party, with Liberal senator Cory Bernardi using the raids to reignite his long-running campaign to ban the burqa.
Senator Lambie again threw her weight behind a burqa ban, labelling it a "national security issue".
"It is like a motorbike helmet. It is like a balaclava," she said. "I will not allow you to wear that into my office because it is a security risk."
Earlier this week, Ms Lambie caused a storm of controversy when she shared a photograph on Facebook of a woman dressed in a burqa and holding a gun.
The far-right UK party Britain First edited the image with a caption saying: "Terror attack level: severe - an attack is highly likely. For security reasons it's now time to ban the burqa."
The woman in the photo is Malalai Kakar, Afghanistan's first female police officer, who was shot dead by extremists in 2008.
The senator was using the photo in a campaign to "ban the burqa" for security reasons after Australia experienced the largest counter-terrorism operation in the country's history on Thursday.
Ms Lambie shared the image posted by far right British group Britain First in response to Senator Cory Bernardi's opposition to the full-length garb worn by some Islamic women.
Ms Lambie has since responded to the controversy, saying it was "a gross over-reaction" and thought Ms Kakar "would be the first to agree with my call to ban the burka (sic)".
"Far from desecrating her memory, my facebook (sic) post honours her and the deadly struggle against brutal thugs and extremists," Ms Lambie wrote in a Letter to the Editor to the ABC.
"As a police officer she would have known how easy it was to conceal weapons or bombs capable of killing large numbers of innocents under a burka. She would have known how much safer it would be in public if the burka was banned."
However, the photographer who took the picture said Ms Kakar would have been outraged.
Lana Slezic said the caption on the photo suggested Ms Kakar was a terrorist, and the use of it by Ms Lambie and Britain First is desecrating her memory.
"Here's a woman whose life was taken by terrorists, extremists in the most horrific way," she said. "She died in front of her son, shot to death outside her home on her way to work.
"Everything she stood for, everything she fought for, for herself, her family, her daughters and future of her country, everything has been desecrated by how Jacqui Lambie and Britain First have used this photograph.
"I'm outraged actually [that] they would steal a photograph without any sort of consent, completely misrepresent it, use it for their own political agendas."
She had tried to contact Lambie and Britain First to ask them to take down the picture and to explain who Kakar was, but she has received no response.
