Integration of LROC NAC and ShadowCam imagery is essential for meter-scale controlled mapping of the entire lunar south pole including Permanently Shadowed Regions (PSRs), but remains challenging due to extreme radiometric differences, sparse overlap across illumination boundaries, and ill-conditioned bundle adjustment networks. This paper proposes a LOLA DEM-mediated multi-source bundle adjustment framework for controlled lunar polar mapping. A hierarchical cross-modality matching strategy is developed using first- and second-order Gaussian steerable gradient features with multi-scale fusion and phase-correlation-based subpixel refinement. Sensor-specific geometric models are established using second-order polynomial transformations for NAC orthoimages and rational polynomial models for ShadowCam map-projected images. Five types of geometric constraints are formulated to integrate intra-sensor, limited cross-sensor, and image-to-DEM observations, with the LOLA DEM acting as a common geometric mediator. To stabilize the heterogeneous network, a hybrid L1-L2 regularization model with adaptive two-stage weighting is optimized using ADMM algorithm. Experiments in the lunar south polar region demonstrate substantial improvements on intra-sensor, cross-sensor, and image-to-reference positioning accuracy. The final seamless 1 m/pixel orthorectified mosaics achieve approximately 5 m absolute accuracy, validating the proposed framework for geometrically unifying illuminated and permanently shadowed terrain in lunar polar controlled mapping.