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The recent spread of Deep Learning (DL) in medical imaging is pushing researchers to explore its suitability for lesion segmentation in Dynamic Contrast-Enhanced Magnetic-Resonance Imaging (DCE-MRI), a complementary imaging procedure increasingly used in breast-cancer analysis. Despite some promising proposed solutions, we argue that a "naive" use of DL may have limited effectiveness as the presence of a contrast agent results in the acquisition of multimodal 4D images requiring thorough processing before training a DL model. We thus propose a pipelined approach where each stage is intended to deal with or to leverage a peculiar characteristic of breast DCE-MRI data: the use of a breast-masking pre-processing to remove non-breast tissues; the use of Three-Time-Points (3TP) slices to effectively highlight contrast agent time course; the application of a motion-correction technique to deal with patient involuntary movements; the leverage of a modified U-Net architecture tailored on the problem; and the introduction of a new "Eras/Epochs" training strategy to handle the unbalanced dataset while performing a strong data augmentation. We compared our pipelined solution against some literature works. The results show that our approach outperforms the competitors by a large margin (+9.13% over our previous solution) while also showing a higher generalization ability.