The three people shot dead at the Castle Sports Complex in Spalding have been named locally.
According to Sky TV sources they are Claire Hart (mother), Charlotte Hart (daughter) and Lance Hart (father).
Earlier an eyewitness told this newspaper the male was aged around late 40s to early 50s and the two female victims were aged about 40 and about 20.
The witness, who was working close by when the incident happened at around 9am, said he heard three shots go off.
He then jumped over a fence to get into the Castle Sports Centre area and he and another man went to help.
Local resident Daniel Chapman tweeted: “Uneasy quiet around town this afternoon despite being Market Day, except for helicopters buzzing overhead.”
A statement read out by Temporary Superintendent Paul Timmins outside Spalding Police Station this afternoon said: “At 9am this morning we received a call reporting a shooting outside Spalding swimming pool on Pinchbeck Road.
“Emergency staff, including police and East Midlands Ambulance Service, responded immediately. At the scene officers found a deceased man along with two women who had received serious injuries.
“CPR was attempted on both women and I am sad to report that both women have died. We believe a shotgun was involved in the incident and are currently investigating the circumstances of this tragic incident.
“We confirm that we are not seeking anyone else in connection with this tragedy.
“I can also confirm that no shots were fired by police and that this is not being treated as a terrorist incident.
“We believe all those involved were known to each other.” Police have not officially identified the victims