In this paper we study the space of strongly Lipschitz (lp,lq)-factorable operators between metric spaces and a Banach spaces. In particular, a factorization of this class through lp and lq spaces is given. We show that this type of operators fits in the theory of composition a-Banach Lipschitz operator ideal. As a special case, we get a Lipschitz version of weakly p-nuclear operators.