Lyme disease is one of the most common infectious vector-borne diseases in the world. In the early stage, the disease manifests itself in most cases with erythema migrans (EM) skin lesions. Better diagnosis of these early forms would allow improving the prognosis by preventing the transition to a severe late form thanks to appropriate antibiotic therapy. Recent studies show that convolutional neural networks (CNNs) perform very well to identify skin lesions from the image but, there is not much work for Lyme disease prediction from EM lesion images. The main objective of this study is to extensively analyze the effectiveness of CNNs for diagnosing Lyme disease from images and to find out the best CNN architecture for the purpose. There is no publicly available EM image dataset for Lyme disease prediction mainly because of privacy concerns. In this study, we utilized an EM dataset consisting of images collected from Clermont-Ferrand University Hospital Center (CF-CHU) of France and the internet. CF-CHU collected the images from several hospitals in France. This dataset was labeled by expert dermatologists and infectiologists from CF-CHU. First, we benchmarked this dataset for twenty-three well-known CNN architectures in terms of predictive performance metrics, computational complexity metrics, and statistical significance tests. Second, to improve the performance of the CNNs, we used transfer learning from ImageNet pre-trained models as well as pre-trained the CNNs with the skin lesion dataset Human Against Machine with 10000 training images (HAM1000). In that process, we searched for the best performing number of layers to unfreeze during transfer learning fine-tuning for each of the CNNs. Third, for model explainability, we utilized Gradient-weighted Class Activation Mapping to visualize the regions of input that are significant to the CNNs for making predictions. Fourth, we provided guidelines for model selection based on predictive performance and computational complexity. Our study confirmed the effectiveness and potential of even some lightweight CNNs to be used for Lyme disease pre-scanner mobile applications. We also made all the trained models publicly available at https://dappem.limos.fr/download.html, which can be used by others for transfer learning and building pre-scanners for Lyme disease.