The family's attorney Arnoldo Casillas said the case is one of racial profiling.
"He assumed that a Mexican-American kid with a gun is a gang member, dressed like a gang member," said Casillas.
Casillas said Lopez was on his way to a friend's house to return the air rifle which he had borrowed.
Sonoma County responded by saying, "Statements in the claims... alleging that the Sheriff 'encourages deputies to prematurely shoot suspects who pose no threat or danger,' are absurd and simply false."
Lopez was shot and killed on October 22 in broad daylight. Two Sonoma County deputies spotted the teen walking. One of them, Erick Gelhaus told investigators he mistook the teen's plastic rifle for a real AK-47. Gelhaus told Santa Rosa police he feared for his life and those around him.
The family ordered its own autopsy which found the first shot fired brought the 13-year-old down.
"It went through his heart. It killed him. He fell to the ground. As he was falling, the officer continued to shoot," said Casillas.
The Federal Bureau of Investigation is conducting an independent investigation.
"We want justice, and then also we want an honest investigation," said Andy's father Francisco Lopez.
Monday, Lopez's family shared pictures of their son who they say was a loving and charismatic boy.
Hundreds have protested the shooting calling it a senseless act.
With regard to the lawsuit, any monetary compensation will be decided by a jury. Casillas won a $24 million judgment after a Los Angeles police officer shot and paralyzed a 13-year-old who was playing cops and robbers.