Lincolnshire Police are appealing for information that may help the investigation into the deaths of Bethany Vincent and Darren Henson.
Bethany, 26, and nine-year-old Darren were tragically found dead at a property on High Holme Road, Louth, on Monday evening.
After a manhunt, officers arrested 29-year-old Daniel Boulton on Tuesday, and he remains in police custody.
Detective Inspector Andy McWatt, from the East Midlands Special Operations Unit, is now appealing for more information relating to the investigation.
He said: "Daniel Boulton may have got a lift from Saltfleetby to Louth on May 31st. If you have information relating to this, please get in touch.
"Our investigation continues at a pace, and even a sighting or any piece of information – however small you think it may be – could prove vital."
Anyone with information can contact the police using the following ways:
Call 101, quoting Incident 445 of 31st May
Contact Crimestoppers, anonymously, on 0800 555111.