Accurate lesion-level segmentation on MRI is critical for multiple sclerosis (MS) diagnosis, prognosis, and disease monitoring. However, current evaluation practices largely rely on semantic segmentation post-processed with connected components (CC), which cannot separate confluent lesions (aggregates of confluent lesion units, CLUs) due to reliance on spatial connectivity. To address this misalignment with clinical needs, we introduce formal definitions of CLUs and associated CLU-aware detection metrics, and include them in an exhaustive instance segmentation evaluation framework. Within this framework, we systematically evaluate CC and post-processing-based Automated Confluent Splitting (ACLS), the only existing methods for lesion instance segmentation in MS. Our analysis reveals that CC consistently underestimates CLU counts, while ACLS tends to oversplit lesions, leading to overestimated lesion counts and reduced precision. To overcome these limitations, we propose ConfLUNet, the first end-to-end instance segmentation framework for MS lesions. ConfLUNet jointly optimizes lesion detection and delineation from a single FLAIR image. Trained on 50 patients, ConfLUNet significantly outperforms CC and ACLS on the held-out test set (n=13) in instance segmentation (Panoptic Quality: 42.0% vs. 37.5%/36.8%; p = 0.017/0.005) and lesion detection (F1: 67.3% vs. 61.6%/59.9%; p = 0.028/0.013). For CLU detection, ConfLUNet achieves the highest F1[CLU] (81.5%), improving recall over CC (+12.5%, p = 0.015) and precision over ACLS (+31.2%, p = 0.003). By combining rigorous definitions, new CLU-aware metrics, a reproducible evaluation framework, and the first dedicated end-to-end model, this work lays the foundation for lesion instance segmentation in MS.