Upon reaching the intersection with US 79 and LA 9 at the courthouse square, LA 2 continued east out of town co-signed with LA 9. The current alignment bypassing Homer to the north was opened in 1964, eliminating the concurrency with LA 9 and creating LA 3062 along the remainder of the bypassed route.
Upon reaching a junction with US 79 and LA 9 at the courthouse square, LA 2 continued eastward out of town, sharing the road with LA 9 until it was rerouted around Homer in 1964. This bypass eliminated the overlap with LA 9 and created LA 3062 for the remaining portion of the route.