Here's an update on this story:
Police say the vehicle was traveling north on SE Evangeline Thurway in the outside lane. The vehicle veered off the road to the right and hit a pedestrian who was walking on the shoulder with the flow of traffic.
The pedestrian, identified as Byron Starks Jr., 29, of Lafayette, died at the scene.
The driver showed no signs of impairment. The crash is still under investigation.
Early Tuesday morning, the Lafayette Police Department responded to a fatal crash in the 1800 block of SE Evangeline Thruway.
A pedestrian was struck and killed by a single-motor vehicle shortly before 5 a.m., according to police.
Traffic Investigators are working to gather details.
We'll keep you updated as more information becomes available.