Police say the man shot his sister around 9:20 a.m. at Country Villa Sheraton Convalescent and Rehabilitation Hospital, located at 9655 Sepulveda Boulevard.
The sister, identified by the LAPD as 58-year-old Lisa Nave, died at the scene. The man was taken into custody at the scene and had a gun with him at the time, police said. Police say the shooting was an apparent mercy killing. Police said Nave came out of a coma four years ago but had remained invalid and in need of close care.
Anderson left the gun on a table next to his sister, police said. He announced he would wait for police on an adjoining patio. Police said no other patients or staff were threatened or confronted by Anderson.
"When the officers arrested him, he's made some statements to the effect of, basically leads us to believe this was seen as, at least in his mind, as a mercy killing," said LAPD Lt. Paul Vernon.
Another woman was found dead at a home on the 26800 block of Claudette Street in Canyon Country, the Los Angeles County Sheriff's Department said. That woman was believed to be the suspect's wife, who reportedly suffered from dementia.
LAPD identified the suspect as Lance Holger Anderson, 60, from Santa Clarita. He was booked on suspicion of the murder of his sister. Anderson is also a suspect in the fatal shooting of his wife, according to police, but there were no immediate charges in that case.
The family of the woman killed at the convalescent home began to worry about the man's wife and called police to do a welfare check. That's when police found the woman dead at the home.
Investigations at both scenes were ongoing.
