The 52-year-old was stabbed up to 12 times at her home in Sandyhill Court, Ballymun. Her body was discovered by neighbours at 3.30pm on Tuesday.
Cllr Keith Connolly said that while he didn’t know Ms Thompson personally, he had visited the scene yesterday where there was a “great sense of shock”.
“Particularly give the graphic nature of the death,” he said. “This is a female, and a middle-aged woman as well, who has died from 11 to 12 stab wounds.
“Obviously the gardai are doing all they can and they had a press briefing there yesterday but the fact that there remains such an open line of inquiry with no real definite answers at the moment has really disturbed people.
“She seems to have been quite quiet and kept to herself but was well known in the area for her role as a youth worker in the past and was quite active in that regard years ago.”
Cllr Connolly added: “I was talking to my colleague Paul McAuliffe and this is the third death of a woman through knife crime in our constituency in the last two years, which is quite harrowing.
"I’ve also spoken to Jim ‘O’Callaghan about this and he is proposing a number of changes around knife crime and mandatory sentences for those caught using a knife to commit crime."
Cllr Connolly said the community "feels for her children and we offer condolences to her family and wider circle of friends.
"I'd also appeal for anyone with information, no matter how small or insignificant, to contact Ballymun Garda station where an incident room has been set up.
"That area is confined and busy enough as well so hopefully someone somewhere will be able to help bring whoever did this awful crime to justice.”
Sunday World has previously revealed that while gardaí continue to keep a “completely open mind” in relation to her death, sources said she may have become “vulnerable” and “inadvertently associated” with local criminal elements due to a change in her lifestyle over the past year.
“Information has come in that this highly respected lady’s life became a bit chaotic in the last few months,” a source said. Because of this situation she may have been in contact with very unsavoury people, which may be who carried out this savage murder.”
Gardaí stressed this was only one line in their detailed enquiries and “every avenue” is being investigated.
Sources said last night that no person of interest had yet been identified and no motive established, despite local reports that two men were seen fleeing from Ms Thompson’s home on Sunday morning.
“What can be confirmed is there was no sign of a break-in or a struggle or fight in her property,” a source said.
This supports a theory that Ms Thompson probably knew her killer.
While the murder weapon is understood to have been recovered, gardaí would not disclose what it is.
Ms Thompson’s two teenage children – a boy and a girl – were not in the property when she was murdered or when her body was found. They were with their father, with whom they have lived for some time.
Superintendent Darren McCarthy of Ballymun Garda Station said: “A family liaison officer has been appointed to Lisa’s family and An Garda Síochána will continue to keep the family informed and support them at this time.
“Lisa was a 52-year-old woman, she was well-known in her local community, which is shocked over the violent and traumatic death.”
Earlier in his statement, Supt McCarthy said that on Tuesday at approximately 3.30pm, gardaí from Ballymun attended a house at Sandyhill Gardens following a call from Dublin Fire Brigade, who were attending at the house in response to a 999 call.
Gardaí discovered the body of Ms Thompson.
Supt McCarthy said last night: “I would like to thank the community for the co-operation and assistance received so far, and information received from across the community continues to assist us in our investigation.
“I appeal to anyone with any information on this violent murder to contact us at Ballymun Garda Station.
“No matter how insignificant you think it may be, we need to hear from you.
“Lisa’s death occurred sometime before the discovery of her body in her home.
“In particular, I am appealing to any person with information on Lisa’s movements from Saturday, May 7 up to Tuesday, May 10 to contact us.
“I am also appealing for any person with any video footage from the Sandyhill area of Ballymun and the surrounding roads of Marewood Crescent, Balbutcher Lane for that period to contact investigating gardaí at Ballymun Garda Station at 01 6664400, the Garda Confidential Line phone number 1800 666 111 or any garda station.”
A cousin of Ms Thompson’s, Nicola Thompson, told the
Sunday World: “Lisa did nothing on anyone (sic). She was a devoted mother and a youth worker. She helped people all her life. This just happened to the wrong person. It is so sad."