DETECTIVES have identified two people who died suddenly and without explanation.
They have named the victims as Olivia Reilly, 29, and 36-year-old Noel Reilly but who are not related.
The pair were found dead at separate locations within a mile of each other in the town.
Ms Reilly’s body was found at a house in the Trasna Way area at about 7.30pm on Sunday.
Paramedics arrived and Ms Reilly was already found to have been dead at the scene.
Then Mr Reilly’s body was discovered at a house in Carrowshee Avenue shortly after midday on Monday.
Police say that all lines of enquiry will be investigated.
A possible link between the deaths is being probed and it is understood that a drugs link is one potential line of enquiry.
Post mortems and toxicology examinations are to be conducted.
Parish priest Father Joseph Mullin said that both families had been left devastated.
“The community is also very disturbed about what has happened,” he added.
“Their mothers and fathers are stunned at the news.”
Politicians said the deaths had left the community very shockedc.
Fermanagh MLA Arlene Foster: “The deaths in Lisnaskea are very concerning.
“The community is shocked by the tragic loss of these two lives. We must remember the families affected.”
UUP MLA Fermanagh & South Tyrone MLA Tom Elliott expressed his shock and sadness.
“At this stage, it is too early to speculate as regards possible causes, but two families and two sets of friends have lost loved ones and will be grieving,” he said.
“Our thoughts are with them at this very sad time.”
Local Sinn Féin councillor Thomas O’Reilly also said that the community was stunned.
“Something like this is very unusual in Fermanagh,” he said.
“This has come as a big shock to the community and the community will be wanting answers as to what happened to these two people.
“My thoughts at this time are with their families.”
PSNI detectives have appealed for anyone with information to contact them in Enniskillen on 0845 600 8000.