The incident was reported shortly before noon on Thursday at a shopping center in the 39800 block of North 10th Street West, according to the Los Angeles County Sheriff's Department.
Investigators said the suspect, who remains in custody and has not been identified, asked one of the victims for car help before a fight reportedly broke out between them.
They said that led to the stabbings.
According to family members, the victims are Ken Evans and his daughter McKenna Evans.
"My heart didn't want it to be true," said Jesse Mercardo, who had been dating McKenna for eight months. "But in my mind, the truth was that she was killed. She is gone now."
Elizabeth Evans, McKenna's mother and Ken's wife, said her husband was in the parking lot working on his car before the attack.
She said she doesn't know why the suspect stabbed him to death.
"When he was in handcuffs, he smirked," she said. "He had a smirk on his face. How dare he? I hope he never gets out of prison."
Both Mercado and the grieving mother want people to know their loved ones were real people with goals.
They said McKenna, who was 22, was studying to be an aesthetician.
"All I want from this is just one more time ... just one more time. Can I just hold her one more time? And say my goodbyes and that's it. Tell her I love her. I'll always love her," said Mercado.
Detectives say the suspect and the victims appeared to have been living in their vehicles.
As they continue to search for a motive, customers like Bonnie Haberstick tell Eyewitness News they're stunned by the leftover crime scene
"It's all the bandages and they are all bloody and gloves and gauze - I mean who does that? Everything was left," she said.
Ben Mihm, a retired detective who owns an independent crime scene cleaning company, also thought this was strange.
"It's always best to clean the scene because you do have to protect from biohazards," he said. "You don't want somebody to walk in there and be stepping into and walking through it."
ABC7 asked the sheriff's department about this and a spokesperson said cleaning protocols are being followed.
Eyewitness News was on the scene when a cleaning company and fire department officials returned to remove the crime debris.
Investigators have not yet found the murder weapon.
The suspect is expected to face murder charges.
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