In the evolving landscape of automated driving systems, the critical role of vehicle localization within the autonomous driving stack is increasingly evident. Traditional reliance on Global Navigation Satellite Systems (GNSS) proves to be inadequate, especially in urban areas where signal obstruction and multipath effects degrade accuracy. Addressing this challenge, this paper details the enhancement of a localization system for autonomous public transport vehicles, focusing on mitigating GNSS errors through the integration of a LiDAR sensor. The approach involves creating a 3D map using the factor graph-based LIO-SAM algorithm, which is further enhanced through the integration of wheel encoder and altitude data. Based on the generated map a LiDAR localization algorithm is used to determine the pose of the vehicle. The FAST-LIO based localization algorithm is enhanced by integrating relative LiDAR Odometry estimates and by using a simple yet effective delay compensation method to enable operation at higher velocities. To robustly fuse LiDAR- and GNSS-based position estimates, an emperical motivated geobased adjustment scheme for the covariances of the two datasources is presented. The performance of the mapping and localization components is validated with real driving data, demonstrating improved stability and accuracy compared to the GNSS-based localization system.