3D lane detection has emerged as a critical challenge in autonomous driving, encompassing identification and localization of lane markings and the 3D road surface. Conventional 3D methods detect lanes from dense birds-eye-viewed (BEV) features, though erroneous transformations often result in a poor feature representation misaligned with the true 3D road surface. While recent sparse lane detectors have surpassed dense BEV approaches, they completely disregard valuable lane-specific priors. Furthermore, existing methods fail to utilize historic lane observations, which yield the potential to resolve ambiguities in situations of poor visibility. To address these challenges, we present SparseLaneSTP, a novel method that integrates both geometric properties of the lane structure and temporal information into a sparse lane transformer. It introduces a new lane-specific spatio-temporal attention mechanism, a continuous lane representation tailored for sparse architectures as well as temporal regularization. Identifying weaknesses of existing 3D lane datasets, we also introduce a precise and consistent 3D lane dataset using a simple yet effective auto-labeling strategy. Our experimental section proves the benefits of our contributions and demonstrates state-of-the-art performance across all detection and error metrics on existing 3D lane detection benchmarks as well as on our novel dataset.