Currently, reliable, robust and ready-to-use CT-based tools for prediction of COVID-19 progression are still lacking. To address this problem, we present DABC-Net, a novel deep learning (DL) tool that combines a 2D U-net for intra-slice spatial information processing, and a recurrent LSTM network to leverage inter-slice context, for automatic volumetric segmentation of lung and pneumonia lesions. We evaluate DABC-Net on more than 10,000 radiologists-labeled CT slices from four different cohorts. Compared to state-of-the-art segmentation tools, DABC-Net is much faster, more robust, and able to estimate segmentation uncertainty. Based only on the first two CT scans within 3 days after admission from 656 longitudinal CT scans, the AUC of our DBAC-Net for disease progression prediction reaches 93%. We release our tool as a GUI for patient-specific prediction of pneumonia progression, to provide clinicians with additional assistance to triage patients at early days after the diagnosis and to optimize the assignment of limited medical resources, which is of particular importance in current critical COVID-19 pandemic.