Mark Jeansonne said his client, Chris Few, had his hands up and was not threatening police when gunfire began.
Two city marshals in Louisiana have been charged with second-degree murder.
The lawyer had not seen the video, but it was described to a judge during a court proceeding on Monday.
The two men opened fire on a car in which the family was riding during a traffic stop in Marksville, Louisiana.
As lawyers gathered at the court, mourners met for Jeremy Mardis' funeral in neighbouring Hattiesburg, Mississippi, from where he had recently moved.
Mr Few meanwhile remained in hospital, unable to attend his son's final service.
He has not been told that his son is dead, the lawyer said.
Col Michael Edmonson of Louisiana state police said on Monday he was still "figuring out" why the father and son's car was being pursued by police.
Hopefully they did not see the boy was in the back seat before they fired, he told CNN.
Early reports said that the two officers were serving a warrant on Mr Few.
However, Mr Edmonson said there was no evidence a warrant was issued, and that no gun was found at the crime scene.
The two officers, Derrick Stafford and Norris Greenhouse, were arrested on Friday after body-camera footage taken from them was assessed.
Referring to the body-camera footage of the incident, Col Edmondson added: "I can tell you, it is the most disturbing thing I've seen, and I'll leave it like that."
They each face charges of second-degree murder and second-degree attempted murder. They are currently being held in a Louisiana jail.
Body camera footage shows that the father of a six-year-old autistic boy was attempting to surrender before police opened fire, killing his son, a lawyer has said.