The Lindt cafe siege gunman Man Haron Monis was "undoubtedly a terrorist" but he was "atypical" in his motivations and behaviour compared with most people who are radicalised to the point of violent extremism, an inquest has heard.

Forensic psychologist and radicalisation expert Kate Barrelle said the taking of hostages and declaring it to be an attack on Australia by Islamic State "was an act of radicalisation by a disturbed man".

The inquest into the deaths of Monis and hostages Tori Johnson and Katrina Dawson has previously heard that Monis had come to be regarded as a "serial pest" to the Australian Security Intelligence Organisation after he provided numerous, useless tip-offs to the spy agency.

Dr Barrelle said scientific tools to predict the radicalisation of particular individuals had yet to be developed and Monis was more of a "lone wolf" compared with most violent extremists who tend to radicalise in a group.

But under intense questioning by the barrister for the Dawson family, Phillip Boulten, SC, Dr Barrelle agreed police and security agencies should have detected Monis was inclined to commit a terrorist attack.

Mr Boulten said in the years leading up to the siege Monis had written "offensive" letters to the families of servicemen and women who had died fighting in the Middle East and had asked the Attorney-General whether it was legal for him to contact IS. He was publicly in favour of an Islamic caliphate and was anti-Zionist.

He was also charged in relation to an alleged murder as well as dozens of sexual assaults against his "spiritual healing" patients.

"I suggest police and security agencies, people who have the responsibility to keep us safe, should have picked up that he was charged with murder ... as a fair predictor of him being inclined to commit a terrorist attack," Mr Boulten said.

"I think that's a very reasonable formulation ... the predictive tools are not there [but] that should not stop people from using their professional judgment," Dr Barrelle said.

"I do agree he did behave like a terrorist ... he was undoubtedly a terrorist."

Earlier on Thursday, Dr Barrelle said Monis "didn't behave like a terrorist but there is no typical behaviour of a terrorist".

Dr Barrelle said that, not only had Monis radicalised, but he had mental health issues including narcissism, paranoia and an anti-social personality. However, he was not psychotic and knew what he was doing.

"It's often suggested [people] are mad or bad - it's not an either/or," she said.

She said Monis probably hoped to survive the siege - and his narcissism would have led him to believe he was likely to survive - but if he was killed "it would have been a positive outcome for his image".

The inquest before coroner Michael Barnes continues.