Firefighters arrived at the single-story house in the 45000 block of Century Circle shortly after 7:30 a.m. Friday and discovered the bodies, according to LASD.
The firefighters had initially responded to a report of a possible gas leak there. Sheriff's deputies were immediately summoned to the scene, where homicide detectives "learned that the deceased male and female both appeared to be suffering from lacerations and stab wounds," a news release said.
Lancaster Mayor Rex Parris confirmed that the two victims were decapitated.
"It doesn't seem to be that the cause of death from the two people inside have anything to do with a gas leak," LASD Lt. Brandon Dean told reporters outside the residence earlier in the day.
One person was transported to a hospital in unknown condition, a Fire Department dispatcher said. That individual's possible injuries were not described.
According to authorities, investigators were questioning a man, a woman and two other children who were also at the home.
LASD later announced Maurice Taylor Sr., 34, was arrested on suspicion of murder and is being held in lieu of $2 million bail.
Anyone with information about the incident is asked to call the sheriff's Homicide Bureau at (323) 890-5500.