The wide spread of coronavirus disease 2019 (COVID-19) has become a global concern and millions of people have been infected. Chest Computed Tomography (CT) imaging is important for screening and diagnosis of this disease, where segmentation of the lung infections plays a critical role for quantitative assessment of the disease progression. Currently, 3D Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance for automatic medical image segmentation tasks. However, most 3D segmentation CNNs have a large set of parameters and huge floating point operations (FLOPs), causing high command for equipments. In this work, we propose LCOV-Net, a lightweight 3D CNN for accurate segmentation of COVID-19 pneumonia lesions from CT volumes. The core component of LCOV-Net is a lightweight attention-based convolutional block (LACB), which consists of a spatiotemporal separable convolution branch to reduce parameters and a lightweight feature calibration branch to improve the learning ability. We combined our LACB module with 3D U-Net as LCOV-Net, and tested our method on a dataset of CT scans of 130 COVID-19 patients for the infection lesion segmentation. Experimental results show that: (1) our LCOV-Net outperforms existing lightweight networks for 3D segmentation and (2) compared with the widely used 3D U-Net, our LCOV-Net improved the Dice score by around 20.36% and reduced the parameter number by 90.16%, leading to 27.93% speedup. Models and code are available at https://github.com/afeizqf/LCOVNet.