The present contribution is the second part of a two-part research work presenting a generic method to extend lift force models that were originally devised for single linear shear flow to arbitrary flow conditions. The method can be applied to the computation of lift forces exerted on prolate spheroidal particles (or fibres) in arbitrary non-uniform flows. The method proposed in the Part I calculates the lift force arising from the dominant streamwise flow shear. In Part II the influence of the non-streamwise flow shear on the lift force is also taken into account. The present method assumes that the particle slip velocity is parallel to the fluid velocity along the particle trajectory. The novelty in the presented method is the computation of the shear lift force model for prolate spheroidal particles taking into account also non-streamwise flow shear. The accuracy of the novel shear lift force model for prolate spheroidal particles is verified by comparing it with the lift force model proposed in Part I via simulating the axial migration of a prolate spheroidal particle in the Poiseuille flow. In order to validate the ability of the present method for capturing the lift component arising from non-streamwise flow shear, the lift force model is compared with established generalised Saffman-type lift models by simulating the motion of a particle in lid-driven cavity flow. The computational results demonstrate that the present lift force model for prolate spheroidal particles is applicable in flow cases with streamwise and non-streamwise flow shear, even if some (reasonably small) accuracy for the case of the streamwise-only shear is lost. (C) 2018 Elsevier Ltd. All rights reserved.