Designing Deep Learning (DL) models for medical image classification tasks poses significant challenges, demanding substantial expertise owing to the intricate nature and critical importance of the undertaking. Creating a DL model tailored for such purposes entails iterative processes of designing, implementing, and fine-tuning algorithms to achieve optimal performance. To mitigate these difficulties, Neural Architecture Search (NAS) has risen as a key field to generate the most effective DL models automatically. However, much of the previous studies involving NAS focus on automating the design of DL models for well-established datasets such as CIFAR-10 and ImageNet. This technique should also be extended to medical image datasets where detecting crucial features accurately in medical images is essential to detect specific illnesses correctly. Therefore, in this study, we investigate NAS to autonomously design best performing DL models for skin lesion detection, thereby demonstrating its usefulness for additional medical image classification endeavours.