Medical image segmentation plays a pivotal role in disease diagnosis and treatment planning, particularly in resource-constrained clinical settings where lightweight and generalizable models are urgently needed. However, existing lightweight models often compromise performance for efficiency and rarely adopt computationally expensive attention mechanisms, severely restricting their global contextual perception capabilities. Additionally, current architectures neglect the channel redundancy issue under the same convolutional kernels in medical imaging, which hinders effective feature extraction. To address these challenges, we propose LGMSNet, a novel lightweight framework based on local and global dual multiscale that achieves state-of-the-art performance with minimal computational overhead. LGMSNet employs heterogeneous intra-layer kernels to extract local high-frequency information while mitigating channel redundancy. In addition, the model integrates sparse transformer-convolutional hybrid branches to capture low-frequency global information. Extensive experiments across six public datasets demonstrate LGMSNet's superiority over existing state-of-the-art methods. In particular, LGMSNet maintains exceptional performance in zero-shot generalization tests on four unseen datasets, underscoring its potential for real-world deployment in resource-limited medical scenarios. The whole project code is in https://github.com/cq-dong/LGMSNet.