Officers said they responded to the home on Deer Ridge Drive around 7 p.m. on Friday and found the father out on the front yard with multiple stab wounds.
A woman, the man's wife and the suspect's mother, was observed through a window inside the living room, investigators said.
Police said the suspect, later identified as Juan Jose Uribe Pelaez, 32, was reportedly inside the home, but was unable to be seen and was not cooperating with officers' demands.
First responders said that thanks to the help of the Galveston County Sheriff's Office, they used a drone to track Uribe Pelaez's movements before officers deployed a Taser and took him into custody.
The parents were rushed to the hospital, where the father was stabilized, but the mother was pronounced dead.
Uribe Pelaez is charged with murder and aggravated assault with a deadly weapon, according to LCPD. His bond was set at half a million dollars.
Investigators confirmed to ABC13 that the suspect is the victims' son.
LCPD said the investigation into the deadly incident remains ongoing and urges anyone with information related to this case is asked to contact them at 281-332-2566.