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Accurate segmentation and classification of lung nodules in computed tomography (CT) scans remains a critical challenge in early lung cancer detection within distributed healthcare Internet of Things (IoT) environments. This paper presents a novel two-stage framework called Adaptive Geometric-Attention Network (AGA-Net) that integrates geometric constraints with multi-scale attention mechanisms for precise nodule segmentation followed by uncertainty-aware malignancy classification in federated learning scenarios. Unlike existing approaches that rely on traditional convolutional architectures, our method introduces a Geometric-Constrained Attention Module (GCAM) that leverages the spherical nature of lung nodules and a Multi-Scale Uncertainty Quantification Network (MUQ-Net) for robust classification under privacy-preserving constraints. The proposed framework demonstrates superior performance across three benchmark datasets: LUNA16, LIDC-IDRI, and NSCLC-Radiomics, achieving a Dice coefficient of 0.927 for segmentation and AUC of 0.951 for malignancy classification while maintaining computational efficiency validated on IoT-class edge hardware including the NVIDIA Jetson AGX Orin and Jetson Orin Nano. The integration of geometric priors with attention mechanisms, uncertainty quantification, and federated learning capabilities provides both high accuracy and clinical interpretability, making it suitable for next-generation computer-aided diagnosis systems deployable on healthcare IoT edge devices.