Lightweight retinal vessel segmentation is important for the early diagnosis of vision-threatening and systemic diseases, especially in a real-world clinical environment with limited computational resources. Although segmentation methods based on deep learning are improving, existing models are still facing challenges of small vessel segmentation and high computational costs. To address these challenges, we proposed a new vascular segmentation network, LFA-Net, which incorporates a newly designed attention module, LiteFusion-Attention. This attention module incorporates residual learning connections, Vision Mamba-inspired dynamics, and modulation-based attention, enabling the model to capture local and global context efficiently and in a lightweight manner. LFA-Net offers high performance with 0.11 million parameters, 0.42 MB memory size, and 4.46 GFLOPs, which make it ideal for resource-constrained environments. We validated our proposed model on DRIVE, STARE, and CHASE_DB with outstanding performance in terms of dice scores of 83.28, 87.44, and 84.50% and Jaccard indices of 72.85, 79.31, and 74.70%, respectively. The code of LFA-Net is available online https://github.com/Mehwish4593/LFA-Net.