Semantic segmentation requires both precise pixel-level labeling and the ability to capture long-range dependencies. Traditional CNNs struggle with global context modeling, while transformers rely on patch embeddings to reduce their quadratic computational costs, sacrificing fine-grained details. Recently, Mamba has emerged as a promising paradigm for long-range dependency modeling with linear complexity. However, its standard serialization disrupts spatial locality, limiting its effectiveness for image-based tasks. To address these limitations, we propose Linked Window Mamba UNet (LWMUNet), which introduces a novel Linked Sliding-Window Serialization (LSWS) mechanism. LSWS transforms the entire image into a single sequence while preserving spatial locality, ensuring both pixel-level precision and global context retention. Furthermore, to accommodate the diverse locality requirements across tasks, we develop Learnable LSWS (L2SWS), enabling adaptive window configurations. The serialized sequence is then processed by Linked Window Mamba, which serves as the encoder of LWMUNet. Experimental results on MoNuSeg, GlaS, and ISIC-2018 demonstrate that LWMUNet surpasses all baselines, achieving Dice scores of 81.27, 92.09, and 91.21, along with superior IoU and HD95 metrics.