Skin cancer is a life-threatening disease where early detection significantly improves patient outcomes. Automated diagnosis from dermoscopic images is challenging due to high intra-class variability and subtle inter-class differences. Many deep learning models operate as "black boxes," limiting clinical trust. In this work, we propose a dual-encoder attention-based framework that leverages both segmented lesions and clinical metadata to enhance skin lesion classification in terms of both accuracy and interpretability. A novel Deep-UNet architecture with Dual Attention Gates (DAG) and Atrous Spatial Pyramid Pooling (ASPP) is first employed to segment lesions. The classification stage uses two DenseNet201 encoders-one on the original image and another on the segmented lesion whose features are fused via multi-head cross-attention. This dual-input design guides the model to focus on salient pathological regions. In addition, a transformer-based module incorporates patient metadata (age, sex, lesion site) into the prediction. We evaluate our approach on the HAM10000 dataset and the ISIC 2018 and 2019 challenges. The proposed method achieves state-of-the-art segmentation performance and significantly improves classification accuracy and average AUC compared to baseline models. To validate our model's reliability, we use Gradient-weighted Class Activation Mapping (Grad-CAM) to generate heatmaps. These visualizations confirm that our model's predictions are based on the lesion area, unlike models that rely on spurious background features. These results demonstrate that integrating precise lesion segmentation and clinical data with attention-based fusion leads to a more accurate and interpretable skin cancer classification model.