Ms Smith went to war-torn Syria in 2015 after converting to Islam.
Dublin has said for months that it has a responsibility to bring Smith back to Ireland and that its main concern was for the safe repatriation of her daughter. "There are sympathies for her daughter - but there is the understanding that Lisa Smith needs to be questioned thoroughly".
"She is now being detained at a south Dublin Garda station under the provisions of Section 30 of the Offences against the State Act, 1939 as amended".
Gardaí (Irish police) say her child is being cared for by relatives.
It's reported in the Irish Independent that Ms. Smith is keen to give her side of the story to investigators.
Irish broadcaster RTE said she was as soon as accompanied by three consular officials from the Department of International Affairs, contributors of the Navy Ranger Flee, and a Turkish safety officer.
Lisa Smith, with a pink blanket over her head, leaving a Turkish Airlines plane at Dublin Airport.
She was met at the rear of the plane by officers and, wearing a pink blanket over her head, was escorted to a Garda vehicle and driven away.
She was transported in a dark-coloured van to Kevin Street Garda station.
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After she traveled to Syria, she reappeared this year with her infant daughter at a Kurdish-controlled displacement camp for wives and children of Islamic State fighters. Ms Smith is originally from Dundalk, Co Louth.
Another Dublin passenger, who asked not to be named, said he recognised her straight away.
The questioning is the culmination of an investigation into the activities of Ms Smith after she left the Defence Forces and took an interest in Isil, initially through online contact.
Varadkar had previously said that a security assessment would need to be carried out to ensure that Smith "does not become a threat to life and limb in Ireland".
The Minister for Justice Charlie Flanagan has described it as "a sensitive case" and said he wanted to reassure people that all relevant state agencies are closely involved.
'A multi-agency network is in plan here comprising agency personnel who select on an ongoing foundation with global colleagues in relation to emerging practice in relation to the complex be concerned of radicalisation.
In Britain, captured British IS fighters will be brought back to the United Kingdom to be put on trial if it is the best place for them to face justice, the national security adviser has said.
The 38-year old can be held for up to three days.