The 52-year-old former youth worker was discovered with multiple injuries, including stab wounds, at her home in Sandyhill Gardens, Ballymun, on May 10.
Gardaí made the first arrests in the case yesterday when they detained a man and a woman on suspicion of murder in a pre-planned operation.
The pair, aged in their 30s, are both from north Dublin and have come to the attention of gardaí in the past.
It is understood that the man in custody was previously known to Ms Thompson and that prior to her death they came into contact once again.
It is understood that the main line of inquiry in the case is whether this man’s partner – who was also arrested yesterday – became jealous of his relationship with the murdered woman.
“This woman isn’t suspected of carrying out the actual murder, but is being investigated for effectively directing her partner to do it,” a source said.
“There had been contact between Ms Thompson and this man before her death, and jealousy may be the motive for this unfortunate woman being killed.”
Gardaí are also probing whether the female suspect helped bring the killer from the scene after the fatal attack.
CCTV footage has been central in establishing who was in the area around the time of the murder, while an analysis of Ms Thompson’s mobile phone contacts has also been key to the inquiry.
In the days after her body was found, gardaí released a statement saying a document linked to Ms Thompson had been left with a civilian member of garda staff and appealed for the person who handed it in to come forward.
The man in question duly presented himself to gardaí, gave a statement to assist the inquiry, and is not a suspect in relation to the murder.
It is understood the man found a driver’s licence on the street and handed it in to gardaí.
Gardaí announced details of the arrests yesterday, saying they had detained “a man and a woman (both 30s) in connection with the murder of Lisa Thompson, whose body was discovered on Tuesday, May 10, 2022 at her home in Sandyhill Gardens, Ballymun, Dublin 11.
“The man and woman are both detained under Section 4 of the Criminal Justice Act, 1984, at separate Dublin Garda Stations.”
The two can be held for a period of up to 24 hours before they must either be charged or released from custody pending a file to the Director of Public Prosecutions (DPP).
In the months before her murder, Ms Thompson had a significant change in personal circumstances and became increasingly more vulnerable as she struggled with escalating personal problems.
She had grown up in the Ballymun area and went to St Joseph’s primary school and on to the local comprehensive school.
Her funeral heard how she was always a friendly and caring person who went on to become involved in youth services.