ROKN has no plans in the foreseeable future to acquire a carrier. LPX(reclassified as LPH) doesn't have the space and capability to operate fixed wing aircrafts. It's well-dock takes up too much space and the hanger deck isn't roomy enough to accommodate fighter jets. At its current size it can only support helo activities.
Although ROKN has continously expressed its desire for at least a small carrier carrying VSTOL planes, there simply DOESN'T exist a plan for it. ROKN is hard pressed to get choppers for its new LPH, they wouldn't have the money to get itself shiny new F-35s or even Harriers for that matter. Besides without nuclear submarines and adequate AAW destroyers carriers wouldn't be worth a ****. SK is in the process of building a capable "escort" force and its Taskforces are likely to be built around Amphibious assets like the LPH rather than a true carrier. Once ROKN has established its surface combatants as fully capable Bluewater navy and acquired enough AIP if not nuclear subs then they can start thinking about carriers. At the moment its just an overly ambitious dream.
are you sure because i rember reading somewhere that the LPXs runway was being covered in Uraethean heat proofing