"Lightning Carriers" has a cool ring to it, but USN amphibious assault ships were carrying AV-8Bs before F-35s came into the fleet, and the Japanese Self Defense Force had helicopter destroyers before the F-35 came around. IOW, carrying F-35s is a functional upgrade of existing ships, not ships built to carry F-35s. Similarly, light carriers and hybrid gunship-carrier ships have been around at least since WW2.