Estimating lighting in indoor scenes is particularly challenging due to diverse distribution of light sources and complexity of scene geometry. Previous methods mainly focused on spatial variability and consistency for a single image or temporal consistency for video sequences. However, these approaches fail to achieve spatio-temporal consistency in video lighting estimation, which restricts applications such as compositing animated models into videos. In this paper, we propose STGlight, a lightweight and effective method for spatio-temporally consistent video lighting estimation, where our network processes a stream of LDR RGB-D video frames while maintaining incrementally updated global representations of both geometry and lighting, enabling the prediction of HDR environment maps at arbitrary locations for each frame. We model indoor lighting with three components: visible light sources providing direct illumination, ambient lighting approximating indirect illumination, and local environment textures producing high-quality specular reflections on glossy objects. To capture spatial-varying lighting, we represent scene geometry with point clouds, which support efficient spatio-temporal fusion and allow us to handle moderately dynamic scenes. To ensure temporal consistency, we apply a transformer-based fusion block that propagates lighting features across frames. Building on this, we further handle dynamic lighting with moving objects or changing light conditions by applying intrinsic decomposition on the point cloud and integrating the decomposed components with a neural fusion module. Experiments show that our online method can effectively predict lighting for any position within the video stream, while maintaining spatial variability and spatio-temporal consistency. Code is available at: https://github.com/nauyihsnehs/STGlight.