In this study, we evaluate the performance of skin lesion classification using ResNet-based convolutional models, focusing on the impact of demographic bias in training data, particularly variations in patient sex and age. We use linear programming to generate datasets with controlled demographic characteristics, allowing systematic investigation of bias effects. Three learning strategies are evaluated: a single-task model, a reinforcing multi-task model, and an adversarial learning scheme. Our sex-based analysis indicates that sex-specific training datasets optimise model performance. Notably, including male patients in the training data improved performance for the male subgroup, even in female-majority cases. Reinforcing and adversarial learning schemes narrowed or eliminated bias gaps in balanced and female-majority datasets. However, these strategies proved less effective in male-majority settings, where models continued to perform better for males than females. The two learning schemes showed marginal bias reduction compared to the baseline model in predominantly male patient populations. Age-based analysis demonstrates comparable baseline performance across the three model approaches, with performance declining across age categories. Younger groups consistently achieve the highest performance, regardless of training data distribution. Although balanced training yields optimal results for the youngest age category, performance decreases in older categories. We find that sex biases arise mainly from data imbalances, while age biases consistently favour younger groups regardless of distribution. These distinct mechanisms require targeted mitigation strategies. Additionally, cross-dataset validation on two external datasets revealed that domain shifts notably affect performance and patterns of demographic bias.