Skin lesion datasets used in the research are highly imbalanced; Generative Adversarial Networks can generate synthetic skin lesion images to solve the class imbalance problem, but it can result in bias and domain shift. Domain shifts in skin lesion datasets can also occur if different instruments or imaging resolutions are used to capture skin lesion images. The deep learning models may not perform well in the presence of bias and domain shift in skin lesion datasets. This work presents a domain adaptation algorithm-based methodology for mitigating the effects of domain shift and bias in skin lesion datasets. Six experiments were performed using two different domain adaptation architectures. The domain adversarial neural network with two gradient reversal layers and VGG13 as a feature extractor achieved the highest accuracy and F1 score of 0.7567 and 0.75, respectively, representing an 18.47% improvement in accuracy over the baseline model.