In this paper, we study Painleve-Kuratowski convergence of the solution sets with a sequence of mappings converges continuously. By considering the solution sets of lexicographic vector equilibrium problems, we establish necessary and/or sufcient conditions to be Hadamard well-posed for the mentioned problems in the sense of Painleve-Kuratowski. The results in this paper unied, generalized and extended some known results in the literature. By obtaining consequences of the results, we also discuss lexicographic variational inequalities as an application.