Automated dermoscopic image analysis has emerged as a critical tool for addressing the global burden of skin cancer, yet two persistent obstacles continue to limit clinical translation: high inter-class morphological similarity among diagnostic categories and severe class imbalance within benchmark datasets such as HAM10000. This paper reviews the methodological evolution of deep learning approaches for multi-class skin lesion classification, tracing the progression from handcrafted feature-based classical machine learning pipelines through deep convolutional architectures, hybrid CNN-recurrent frameworks, and Vision Transformer-based models. Particular attention is given to the gate desynchronisation limitation inherent in standard Long Short-Term Memory units, which excludes the internal cell state from gate computations and can cause premature loss of diagnostically relevant sequential information. The review further examines loss-level and data-level strategies for class-imbalance mitigation, including Weighted Cross-Entropy, Focal Loss, SMOTE, and generative adversarial augmentation, and surveys the explainability frameworks required for regulatory and clinical acceptance. Based on the gaps identified, the paper discusses an emerging direction—class-balanced hybrid CNN-Peephole LSTM frameworks—and outlines future research priorities, including attention-based feature filtering, multi-modal metadata fusion, and Vision Transformer knowledge distillation for resource-constrained clinical deployment.