The chest radiography is one of the most accessible radiological examinations for diagnosis of lung and heart diseases. Deep learning techniques have been increasingly used to provide more accurate detection of thorax lesions on Chest X-Ray (CXR) images. However, we observe that we can use the complementarity of dual asymmetric deep convolutional neural networks (DCNNs) to improve the ability of CXR image classification compared to the single network. In this paper, we propose a novel dual lesion attention network named DuaLAnet for the classification of 14 thorax diseases on chest radiography. The DuaLAnet consists of two asymmetric attention networks, DenseNet-169 and ResNet-152, to integrate the advantages into a wider architecture, thus extracting more discriminative features of different abnormalities from the raw CXRs. Moreover, a training strategy is designed to integrate the loss contribution of the involved classifiers into a unified loss. The proposed DuaLAnet has been evaluated against eight deep learning models using the patient-wise official split of the ChestX-ray14 dataset [1]. Our results show that DuaLAnet achieves and average per-class AUC of 0.820 in the experiments, which clearly substantiate the effectiveness of DuaLAnet when compared to the state-of-the-art baselines.