The automatic analysis of endoscopic images to assist endoscopists in accurately identifying the types and locations of esophageal lesions remains a challenge. In this paper, we propose a novel multi-task deep learning model for automatic diagnosis, which does not simply replace the role of endoscopists in decision making, because endoscopists are expected to correct the false results predicted by the diagnosis system if more supporting information is provided. In order to help endoscopists improve the diagnosis accuracy in identifying the types of lesions, an image retrieval module is added in the classification task to provide an additional confidence level of the predicted types of esophageal lesions. In addition, a mutual attention module is added in the segmentation task to improve its performance in determining the locations of esophageal lesions. The proposed model is evaluated and compared with other deep learning models using a dataset of 1003 endoscopic images, including 290 esophageal cancer, 473 esophagitis, and 240 normal. The experimental results show the promising performance of our model with a high accuracy of 96.76% for the classification and a Dice coefficient of 82.47% for the segmentation. Consequently, the proposed multi-task deep learning model can be an effective tool to help endoscopists in judging esophageal lesions.