Compared to natural images, medical images usually show stronger visual patterns and therefore this adds flexibility and elasticity to resource-limited clinical applications by injecting proper priors into neural networks. In this paper, we propose spatially covariant pixel-aligned classifier (SCP) to improve the computational efficiency and meantime maintain or increase accuracy for lesion segmentation. SCP relaxes the spatial invariance constraint imposed by convolutional operations and optimizes an underlying implicit function that maps image coordinates to network weights, the parameters of which are obtained along with the backbone network training and later used for generating network weights to capture spatially covariant contextual information. We demonstrate the effectiveness and efficiency of the proposed SCP using two lesion segmentation tasks from different imaging modalities: white matter hyperintensity segmentation in magnetic resonance imaging and liver tumor segmentation in contrast-enhanced abdominal computerized tomography. The network using SCP has achieved 23.8, 64.9 and 74.7 reduction in GPU memory usage, FLOPs, and network size with similar or better accuracy for lesion segmentation.