Lincolnshire Police launched an urgent appeal to find Daniel Boulton, 29, after Ms Vincent and Darren were found dead at a property in High Holme Road just before 8.30pm on Monday.Boulton was detained by officers in the Hubbard's Hill area at around 12 noon on Tuesday.
He remains in police custody and is being questioned in connection with the murders of Ms Vincent and Darren- who were both found with multiple stab injuries. He is also being questioned on suspicion of injuring an off-duty police officer.
Another young child was found uninjured at the property.
Lincolnshire Police’s Head of Crime, Detective Chief Superintendent Andy Cox, said: “This has been a tragic, extraordinary, and worrying set of circumstances in equal measure. A woman and child have lost their lives in the most devastating way and I know that their loved ones will be feeling the magnitude of that today and our thoughts go out to them.
“We have also seen communities in Louth, and indeed further afield, who will undoubtedly have been anxious about the possible danger in the town since last night. To all of you I want to say thank you. You have been listening to our safety advice and sharing our appeals, all of which has helped us to do our job to the best of our ability.
“We are also aware of speculation on social media. I would like to ask the public to please refrain from speculating as this is an ongoing investigation.
“We will release further details when we are in a position to do so.
"We are continuing to appeal for anyone who can assist us with our investigation to contact us on 101."