Authorities responded to a call that a man was threatening a woman with a weapon during a possible robbery on the 3400 block of South Broadway at about 8 a.m.
LAPD Sgt. Mitzi Fierro said when officers kicked the door open at the location, they saw the suspect, a man in his 40s, holding a knife to a woman's neck, and the woman was bleeding from her neck.
According to police, the woman was trying to fight her boyfriend off after he came at her with a knife. She suffered multiple stab wounds.
When officers ordered him to drop the weapon, they said he let go of the woman and lunged at them. At least one officer opened fire, killing the suspect.
The suspect's name was not released.
"It's kind of one of those situations where we hope that our officers do the right thing and take whatever precautions they can to preserve life and prevent injury," Fierro said.
The incident forced William Jefferson Clinton Middle School, a nearby charter school, to lock down.
"We don't normally have stuff like this happen over here, so it's kind of shocking," said Ken Stone, plant manager of Clinton Middle School. "You don't want to see anyone lose their life, kind of shook up over that. But other than that it's pretty safe around here."
The victim was hospitalized with knife wounds to her face, neck, hands and arms, as well as a head injury.