Set-valued optimization which is an extension of vector optimization to set-valued problems is a growing branch of applied mathematics. The application of vector optimization technics to set-valued problems and the investigation of optimality conditions has been of enormous interest in the research of optimization problems. In this paper we have considered a Mayer type problem governed by a discrete inclusion system with Lipschitzian set-valued mappings. A necessary condition for K-optimal solutions of the problem is given via local approximations which is considered the lower and upper tangent cones of a set and the lower derivative of the set-valued mappings