We present an automatic method for joint liver lesion segmentation and classification using a hierarchical fine-tuning framework. Our dataset is small, containing 332 2-D CT examinations with lesion annotated into 3 lesion types: cysts, hemangiomas, and metastases. Using a cascaded U-net that performs segmentation and classification simultaneously, we trained a strong lesion segmentation model on the dataset of MICCAI 2017 Liver Tumor Segmentation (LiTS) Challenge. We used the trained weights to fine-tune a slightly modified model to obtain improved lesion segmentation and classification, on the smaller dataset. Since pre-training was done with similar data on a related task, we were able to learn more representative features (especially higher-level features in the U-Net's encoder), and improve pixel-wise classification results. We show an improvement of over 10% in Dice score and classification accuracy, compared to a baseline model. We further improve the classification performance by hierarchically freezing the encoder part of the network and achieve an improvement of over 15% in Dice score and classification accuracy. We compare our results with an existing method and show an improvement of 14% in the success rate and 12% in the classification accuracy.