Liver cancer has high morbidity and mortality rates in the world. Multi-phase CT is a main medical imaging modality for detecting/identifying and diagnosing liver tumors. Automatically detecting and classifying liver lesions in CT images have the potential to improve the clinical workflow. This task remains challenging due to liver lesions' large variations in size, appearance, image contrast, and the complexities of tumor types or subtypes. In this work, we customize a multi-object labeling tool for multi-phase CT images, which is used to curate a large-scale dataset containing 1,631 patients with four-phase CT images, multi-organ masks, and multi-lesion (six major types of liver lesions confirmed by pathology) masks. We develop a two-stage liver lesion detection pipeline, where the high-sensitivity detecting algorithms in the first stage discover as many lesion proposals as possible, and the lesion-reclassification algorithms in the second stage remove as many false alarms as possible. The multi-sensitivity lesion detection algorithm maximizes the information utilization of the individual probability maps of segmentation, and the lesion-shuffle augmentation effectively explores the texture contrast between lesions and the liver. Independently tested on 331 patient cases, the proposed model achieves high sensitivity and specificity for malignancy classification in the multi-phase contrast-enhanced CT (99.2%, 97.1%, diagnosis setting) and in the noncontrast CT (97.3%, 95.7%, screening setting).