The LC and the LX do not have the same front end sheet metal. Differences are minor but definite. You may or may not have issues, depending on which bumper you choose. The LX is also different from the LX in that the grille is attached to the hood and requires additional clearance when opening. This could be an issue if you go with a bumper that has a bull bar.
The only bars I can think of that match your criteria are the
Dobinsons, the
ARB Sahara and, at a distant 3rd, the
So-Flo. For a few dollars more, you can get the Ironman Commercial Deluxe, which is a great bumper for the money.