It's not just the rear lower bumper panel that is different - the rear suspension on the GT is independent arms, while the rear suspension on LXS, EX, S, and GT-Line models have a solid rear axle. The trunk floor is also different (where the spare tire sits) - to allow for the independent rear suspension on the GT. The exhaust pipe routing is different. Because of this the available GT exhausts will not fit on the non-GT models.
If you were to install the lower panel from a GT on your LXS you would have to get an exhaust shop to fabricate a dual-outlet exhaust. I don't know of anyone who has tried this.