Rapid and accurate flood extent mapping is critical for disaster response and mitigation. Synthetic Aperture Radar (SAR) imagery from Sentinel-1 enables all-weather, all-day flood monitoring; however, existing deep learning approaches often rely on architectures with millions of parameters, which may constrain their use in time-sensitive or resource-limited flood-mapping workflows. We propose LightFloodNet, a lightweight encoder-decoder network that integrates established CBAM attention mechanisms and depthwise separable convolutions within a U-Net-inspired framework as a computationally efficient candidate for SAR flood segmentation. On the geographically unseen test regions of the Sen1Floods11 benchmark, the proposed model achieves an IoU of 0.5399 and precision of 0.7554 using only 1.57 million parameters, approximately five times fewer than a standard U-Net baseline. It maintains comparable segmentation performance while attaining higher precision (+0.104) and a 29-fold reduction in computational cost relative to the same baseline. A systematic ablation study shows that Tversky Loss mainly improves recall, CBAM primarily shifts predictions toward higher precision, and Test-Time Augmentation provides small but consistent inference gains. The results indicate that the proposed architecture is a promising candidate for near-real-time SAR flood mapping in resource-constrained settings, pending hardware-specific validation.