Summary: The aim of this paper is to investigate the generalized well-posedness with perturbation of set optimization problems (SOP) in terms of lower set less order relation. Based on the lower set less order relation, we introduce the notion of generalized well-posedness with perturbation of (SOP). Then the relationships between the generalized well-posedness with perturbation and the well-setness with perturbation of (SOP) are established under some suitable assumptions. We also present the sufficient conditions for the generalized well-posedness with perturbation and well-setness with perturbation. Moreover, we obtain the relationships between semicontinuity of minimal solution mappings of a parametric set optimization problem and the generalized well-posedness with perturbation of (SOP). Finally, the equivalence between the generalized well-posedness with perturbation of (SOP) and the generalized well-posedness with perturbation of a corresponding scalar optimization problem is derived by using the scalarization method.