Officers were called by the ambulance service shortly after 12:30am last Saturday (December 2), to an address in Buttermere Avenue, Morcambe, where paramedics were treating a woman with facial injuries.
The 29-year-old woman told police she had walked into her living room after hearing a knock at the window.
She then heard a loud bang, the window shattered and she was hit in the face.
She was taken to hospital for treatment to facial injuries caused by what is believed to be shotgun pellets.
Her injuries are serious but not life-threatening.
Following further investigation, four people were arrested by police yesterday (Saturday, December 9) in the West Yorkshire area.
A 25-year-old man from Huddersfield was arrested on suspicion of attempted murder and is currently in custody.
Three more people - a man aged 21 and two women aged 27 and 25 - all from Huddersfield were arrested on suspicion of assisting an offender and are currently in custody.
Det Supt Simon Giles, of Lancashire Police, said: “This remains a fast-moving and active investigation following an extremely serious incident in Morecambe.
"It is only a matter of luck the victim was not more seriously hurt or even killed. We have made a number of further arrests to try and establish who is responsible.
“While I do believe this was an isolated incident and there is no threat to the wider community I understand that this may cause some concern and I’d reassure the public that we have a major investigation running in order to locate and arrest those responsible.”
Five people - three men and two women - arrested on suspicion of attempted murder at the time of the offence have been bailed pending further enquiries.
Anyone with information about the incident can contact police on 101 quoting log number 0035 of Saturday December 2.
Alternatively they can contact independent charity Crimestoppers on 0800 555 111.