I did it in my Sport a few years back, one of my favorite trails ever. Most of the trail is actually not as tough as you'd think by its rating (there is a nice "gatekeeper" at the very entrance of the trail, if you make it through that rocky ledge you should be good to go the whole way through), I think it gets its degree of Difficult because of the famous staircase near the very end, which can be a bit unsettling for newbies due to how steep it is when you get to the top. Just follow the tire marks of the thousands of vehicles that drove down and carefully modulate your brakes, it looks worse than it is and you may not even need a spotter (although someone to tell you when your tires are about to drop down another step would definitely help.)
You should make it through with no drama and no risk of damaging anything with your stock LR4. I had oversized 18s on my Sport and rock sliders, no lift, when I did it last. The slider never got close to scraping anything and the approach and departure angles of our cars in off road height, plus the smidgen of extra clearance from our beefier 18" ers, are just about perfect to negotiate all those ledges. As long as it is dry, that slickrock affords incredible traction until you are just about vertical. You will love that trail I am sure, make sure you don't miss the several on-foot detours along the way for some incredible views.
