Daniel Boulton has been found guilty of murdering Bethany Vincent and her son Darren Henson.
A jury at Lincoln Crown Court took just over two hours to decide that their killings on May 31 last year was fact murder.
Ms Vincent and Darren, known to his family as DJ, were both found stabbed to death at their home in High Holme Road, Louth, shortly after 8pm on May 31.
Read more court news here
Twelve jurors have heard over two weeks of harrowing evidence at Lincoln Crown Court.
The jury heard Boulton carried out the killings after walking 28 miles from his hostel in Alexandra Road, Skegness.
Boulton then led police on a manhunt until the following day, burgling a cottage where he stole alcohol and food, and assaulting an off-duty police officer in the leg in the Hubbard’s Hills area of Louth.
He was Tasered and arrested at a nearby farm in Hallington after trying to get into two cars and encouraging armed officers to shoot him.
Boulton, 30, admitted their manslaughter but denied murder. His defense had argued Boulton’s personality disorder caused him to lose control and carry out the killings.
Mr Justice Pepperall told Boulton: “For the brutal murders of Bethany Vincent and her son Darren Henson, 9, there is only one sentence of life in prison on both counts.
He will have to decide if the sentence will carry a minimum term or carry a whole life sentence.
Sentencing is expected tomorrow, Wednesday February 2nd.
To sign up for the Hull Live newsletter, click here