Skin lesion prediction using artificial intelligence (AI) models is highly dependent on skin tone, yet current approaches largely overlook this critical factor. The Fitzpatrick 17k dataset, which contains six skin tone categories: lighter to darker, is severely imbalanced, with most models biased toward lighter skin tones. Previous efforts to improve overall accuracy fall short: overall accuracy fails to reflect true performance across imbalances. This creates a significant gap, as effective skin lesion detection must work across all skin tones, not just a few. To address this, we introduce the Cost-Aware EfficientNet (CAEN) model, combining cost-sensitive learning (CSL) and attention mechanisms to tackle imbalanced data and ensure the model generalizes well across all skin tones with detailed interpretability. Rather than simply improving accuracy, our model enhances class-specific performance, achieving 79% recall for non-neoplastic, 88% for benign, and 80% for malignant lesions. This indicates an overall improvement in darker tones of approximately 44.55% compared to state-of-the-art results from prior studies. Furthermore, it remains robust across augmented test conditions, such as changes in brightness, contrast, blur, and zoom, providing balanced outcomes for diverse skin tones. This novel approach offers a significant leap toward fair and reliable skin lesion prediction for all skin tones with interpretability.