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Large-scale datasets with high-quality labels are desired for training accurate deep learning models. However, due to the annotation cost, datasets in medical imaging are often either partially-labeled or small. For example, DeepLesion is such a large-scale CT image dataset with lesions of various types, but it also has many unlabeled lesions (missing annotations). When training a lesion detector on a partially-labeled dataset, the missing annotations will generate incorrect negative signals and degrade the performance. Besides DeepLesion, there are several small single-type datasets, such as LUNA for lung nodules and LiTS for liver tumors. These datasets have heterogeneous label scopes, i.e., different lesion types are labeled in different datasets with other types ignored. In this work, we aim to develop a universal lesion detection algorithm to detect a variety of lesions. The problem of heterogeneous and partial labels is tackled. First, we build a simple yet effective lesion detection framework named Lesion ENSemble (LENS). LENS can efficiently learn from multiple heterogeneous lesion datasets in a multi-task fashion and leverage their synergy by proposal fusion. Next, we propose strategies to mine missing annotations from partially-labeled datasets by exploiting clinical prior knowledge and cross-dataset knowledge transfer. Finally, we train our framework on four public lesion datasets and evaluate it on 800 manually-labeled sub-volumes in DeepLesion. Our method brings a relative improvement of 49% compared to the current state-of-the-art approach in the metric of average sensitivity. We have publicly released our manual 3D annotations of DeepLesion in https://github.com/viggin/DeepLesion_manual_test_set.