One Stop shop for Daily Digest - News, Views and analysis of the political developments of the Horn of Africa. Now you can follow by email alerts situated at the bottom. Please feel free to forward any item of interest - it is your blog too (Make it your Home Page)
Police also searched a house in the village of Moulton, five miles (8km) from the centre of Spalding.
Speaking on BBC Radio Lincolnshire, the leader of South Holland District Council said he had been told it was believed to be a "domestic incident".
"This looks by all accounts to be a very tragic family incident", Councillor Gary Porter said.
East Midlands Ambulance Service said paramedics were told to approach the scene with caution and fought to save the three people, who had gunshot wounds.
The air ambulance was also called to the swimming pool.
"Despite the best efforts of everyone at the scene the patients were pronounced dead", an ambulance spokesperson said.
Any witnesses have been asked to contact police.
The leisure centre said it had closed because of the shooting.
Lincolnshire County Council said pupils were being kept inside local schools for safety, but the lockdown had since been lifted.
One local woman, who asked not to be named, said: "We heard all the police cars earlier this morning - they were absolutely everywhere, tearing around.
"We didn't hear any shots, nothing at all, only the dozens, literally dozens, of police cars."
District councillor Gary Taylor, who represents Spalding Castle ward, said: "It's terrible news and local people are very shocked. It's a very quiet place, gun crime does not exist in this area at all."
Labour leader Jeremy Corbyn tweeted: "Shocking events in Spalding, Lincolnshire. My thoughts are with the victims and their families."