k-lp-Lipschitz t-norms

k-lp-Lipschitz t-norms are shown to be ordinal sums of k-lp-Lipschitz Archimedean t-norms. Additive generators of k-lp-Lipschitz t-norms are characterized by means of k-p-convexity. Several necessary and sufficient conditions for a function to be a k-p-convex additive generator are also given.