Hey Justin, that's not just the matter of LEDs, as the Limited edition features built-in fiber optics, which is rather about the headlight construction, than about the bulbs. So by just replacing the tail light bulbs with LEDs you will not gain that look.
However, LED bulbs last longer and look more attractive in the tail lights, so you may want to swap the tail light bulbs to LEDs on your Elantra. However, that change will not make your tail lights look like the Limited Edition ones.
Here are some ideas of quality LED bulbs for your Elantra: 2017 Hyundai Elantra LED lights at CARiD
Hope this helps!