The victim has been identified as Charles Thomas, 60, of Lafayette.
Robert Wayne Thomas, 50, of Lafayette has been arrested and charged with one count of second-degree murder, authorities said. He was booked into the Lafayette Parish Correctional Center.
The victim and suspect are not related, according to LPD.
LPD said the victim and suspect got into a fight near a Shell station on Evangeline Thruway. LPD said Thomas was hit and fell in the roadway, hitting his head.
LPD said that around 9:27 a.m., authorities responded to the 2000 block of NW Evangeline Thruway in reference to a man lying on Frontage Road.
According to LPD, a passerby started CPR on the victim until medical personnel arrived, but the victim was later pronounced dead at the scene.
This investigation is ongoing and LPD urges anyone with information regarding the incident to contact Crime Stoppers at 337-232-TIPS.
Updates will follow as information is released.