Gaussian splatting techniques have recently revolutionized outdoor scene decomposition and relighting through multi-view images. However, achieving high rendering quality still requires a fixed lighting condition among all input views, which is costly or even impractical to capture in outdoor scenes. In this paper, we propose outdoor scene decomposition and relighting with 2D Gaussian splatting (OSDR-GS), a novel inverse rendering strategy under outdoor changing and unknown lighting conditions. Firstly, we present a lighting-based group learning framework that categorizes input images into multiple lighting groups, to learn the separate lighting from each group individually. Secondly, OSDR-GS introduces a fine-grained outdoor lighting component to represent sun-light and sky-light, respectively, which are also adjusted via the correlative exposure factors adaptively. Finally, we construct a visibility-driven shadow module to characterize the nuanced interplay of light and occlusion realistically, for eliminating the uncertainty of dark pixels on lighting-based group learning. Extensive experiments on multiple challenging outdoor datasets validate the effectiveness of OSDR-GS, which achieves the state-of-the-art performance in changing lighting scene inverse rendering.