Lebanese Interior Minister Nohad Machnouk says one of the men's brothers, Tareq Khayat, moved to the Isis stronghold of Raqqa in Syria and become a commander in the jihadist group more than a year ago, Reuters reports.
Lebanon's Internal Security Force then placed the trio and a fourth brother Amer Khayat, under surveillance.
Khaled, Mahmoud and Amer Khayat were all living in Australia but sometimes visited Lebanon, Machnouk said in Beirut.
Machnouk said Amer Khayat had arrived in Lebanon on July 15, the day Australian police allege plotters tried to smuggle a bomb on to a flight from Sydney to Abu Dhabi.
Australian police have previously said a man had tried to check in luggage without knowing it contained a bomb, hidden in a meat grinder, given to him by one of his brothers.
Machnouk said a bomb had also been hidden in a large child's doll in the luggage.
He did not say what has happened to Amer Khayat.
The plot was foiled because the luggage exceeded the airline's weight limit, Machnouk said.
Australian police have previously said it appeared one of the accused had left the airport, taking the luggage with him, while his brother boarded the plane and left Australia.
When asked whether the operation would have been successful if the luggage had not exceeded the weight limit, Machnouk said: "Probably, yes".
He added information offered by Lebanese intelligence had "assisted in foiling a large operation aiming to blow up a plane".
- AAP