Shaw said Thursday at a news conference that an arrest warrant has been issued for 27-year-old Grover Cannon, who was already wanted on a charge of attempted second-degree murder.
Once arrested, Shaw says Cannon will be booked with first-degree murder.
Shaw says Lavalley was taken to University Health, where he died a short time later.
Police spokesman Bill Goodin says Shreveport police, Caddo Parish deputies, along with DeSoto Parish deputies, U.S. Marshals and the state police have joined the search for Cannon.