Automatic detection of liver lesions in CT images poses a great challenge for researchers. In this work we present a deep learning approach that models explicitly the variability within the non-lesion class, based on prior knowledge of the data, to support an automated lesion detection system. A multi-class convolutional neural network (CNN) is proposed to categorize input image patches into sub-categories of boundary and interior patches, the decisions of which are fused to reach a binary lesion vs non-lesion decision. For validation of our system, we use CT images of 132 livers and 498 lesions. Our approach shows highly improved detection results that outperform the state-of-the-art fully convolutional network. Automated computerized tools, as shown in this work, have the potential in the future to support the radiologists towards improved detection.