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Automatic lung lesions segmentation of chest CT scans is considered a pivotal stage towards accurate diagnosis and severity measurement of COVID-19. Traditional U-shaped encoder-decoder architecture and its variants suffer from diminutions of contextual information in pooling/upsampling operations with increased semantic gaps among encoded and decoded feature maps as well as instigate vanishing gradient problems for its sequential gradient propagation that result in sub-optimal performance. Moreover, operating with 3D CT-volume poses further limitations due to the exponential increase of computational complexity making the optimization difficult. In this paper, an automated COVID-19 lesion segmentation scheme is proposed utilizing a highly efficient neural network architecture, namely CovSegNet, to overcome these limitations. Additionally, a two-phase training scheme is introduced where a deeper 2D-network is employed for generating ROI-enhanced CT-volume followed by a shallower 3D-network for further enhancement with more contextual information without increasing computational burden. Along with the traditional vertical expansion of Unet, we have introduced horizontal expansion with multi-stage encoder-decoder modules for achieving optimum performance. Additionally, multi-scale feature maps are integrated into the scale transition process to overcome the loss of contextual information. Moreover, a multi-scale fusion module is introduced with a pyramid fusion scheme to reduce the semantic gaps between subsequent encoder/decoder modules while facilitating the parallel optimization for efficient gradient propagation. Outstanding performances have been achieved in three publicly available datasets that largely outperform other state-of-the-art approaches. The proposed scheme can be easily extended for achieving optimum segmentation performances in a wide variety of applications.