We present a model that fuses instance segmentation, Long Short-Term Memory Network and Attention mechanism to predict COVID-19 and segment chest CT scans. The model works by extracting a sequence of Regions of Interest that contain class-relevant information, and applies two Long Short-Term Memory networks with attention to this sequence to extract class-relevant features. The model is trained in one shot: both segmentation and classification branches, using two different sets of data. We achieve a 95.74% COVID-19 sensitivity, 98.13% Common Pneumonia sensitivity, 99.27% Control sensitivity and 98.15% class-adjusted F1 score on the main dataset of 21191 chest CT scan slices, and also run a number of ablation studies in which we achieve 97.73% COVID-19 sensitivity and 98.41% F1 score. All source code and models are available on https://github.com/AlexTS1980/COVID-LSTM-Attention.