The incident occurred on the 5700 block of 9th Avenue around 6:50 a.m.
Detectives say the dispute started over a bill between roommates. They say one of the roommates shot and killed 40-year-old Terry Smith and wounded her boyfriend.
The suspect was treated for stab wounds he suffered during the altercation.
"He'll be booked for murder and attempted murder before the days end," said LAPD Detective Chris Barling. His name was not released.
Derrick Jamison says he is one of about eight people who live in the home. He says it is a transitional home for people like him trying to get back on their feet. He says he was in the bathroom when he heard gunfire.
"It's a sad thing, it's something that should not have come about," said Jamison, adding that the bill was only about $8 or $9.
Arzon White, a friend of the woman, said the female victim had two children, a boy and a girl.
"She just had a boy about a year ago. She was single, working," White said in tears. "But I don't know what happened."