Three fire crews from St Annes and Lytham attended the latest incident at the property on Heyhouses Lane at around 2.30am today.
Conservatory doors at the back were set alight as an elderly couple and their daughter slept.
Det sgt Paddy Dowling, of Blackpool CID, said: "We obviously suspect or believe it is linked to the first attack and have got various lines of inquiry we are pursuing."
On Thursday, October 9, the front door of the property was damaged after a fire was deliberately started. The family were at home at the time.
Police said they were no longer looking for a small white car or van which was seen in the area at the time of this morning's attack.
Det sgt Dowling said: "They have been traced and eliminated form our inquiries."
Watch manager firefighter Steven Arnold said the occupants were "very shocked and distressed".
He said: "It's the second fire we've had in that premises in just over a week. Both fires were of suspicious origin and are being investigated by the police."
John Taylor, media officer for Lancashire Fire and Rescue Service, said: "We would deplore any fire started that clearly can devastate lives and take life."
He described it as "despicable".