Purpose: To investigate the efficacy of Fluid and White Matter Suppression (FLAWS) MRI sequence in improving Deep Learning (DL)-based detection and segmentation of cortical lesions in Multiple Sclerosis (MS) patients even, and to develop models that can generalize to clinical settings where only standard T1-weighted images (MPRAGE) are available. Materials and Methods: In this multi-site study, we analyzed 204 MS patients using DL models developed with FLAWS and Magnetization Prepared 2 Rapid Acquisition Gradient Echoes (MP2RAGE) sequences. Reference standard annotations were established through two approaches: (1) consensus of three expert raters across all contrasts, and (2) single-rater annotations for individual modalities. Models were validated on both internal and external datasets, with performance assessed using F1-score for detection and DSC for segmentation accuracy. Results: Models involving FLAWS demonstrated superior performance over MP2RAGE-only models. The model combining MP2RAGE and FLAWS achieved CL detection with median F1-score of 0.667[0.339−0.840] compared to multi-rater consensus. Models trained on comprehensive consensus annotations outperformed those trained on single-modality annotations. Notably, a model trained on MP2RAGE but leveraging FLAWS-derived annotations showed strong generalization when applied to standard clinical Magnetization Prepared Rapid Gradient-Echo (MPRAGE) datasets from a different institution (median F1-score: 0.55[0.211−0.998]), demonstrating successful knowledge transfer from advanced research sequences to routine clinical sequences. Conclusion: Integration of FLAWS-derived contrasts and annotations significantly improves DL-based CL detection and segmentation. The models demonstrate capability in identifying lesions missed by individual raters and maintain robust performance when applied to standard clinical sequences at external sites. This cross-sequence generalization facilitates immediate clinical translation, supported by publicly available inference models on DockerHub.