The 26-year-old woman and the boy were found stabbed at a home in High Holme Road, Louth, on Monday evening.
Another young child was found uninjured at the property, Lincolnshire Police said.
Daniel Boulton, 29, who was known to both victims, is wanted for questioning. The force urged the public not to approach him.
A knife believed to have been used to inflict multiple stab wounds upon both victims was recovered at the scene, officers said.
Det Ch Supt Andy Cox said speculation about an abduction was incorrect and the child found at the scene was safe.
“We are urgently seeking assistance to locate and arrest Daniel Boulton. Please, do not approach him as he could be potentially dangerous,” he said.
“We are not looking for anyone else in connection with this incident at present.”
Floral tributes have been left at the scene, with well-wishers seen handing bouquets to officers stationed behind a police cordon.
One was left by Chantelle Fenton, who lives in the town.
“I saw the lady a few times when I walked past but I never knew her,” she said.
“It’s just sad because it’s happened on your own doorstep.”