Background: Early and accurate detection of COVID-19-related findings (such as well-aerated regions, ground-glass opacity, crazy paving and linear opacities, and consolidation in lung computed tomography (CT) scan) is crucial for preventive measures and treatment. However, the visual assessment of lung CT scans is a time-consuming process particularly in case of trivial lesions and requires medical specialists. Method: A recent breakthrough in deep learning methods has boosted the diagnostic capability of computer-aided diagnosis (CAD) systems and further aided health professionals in making effective diagnostic decisions. In this study, we propose a domain-adaptive CAD framework, namely the dilated aggregation-based lightweight network (DAL-Net), for effective recognition of trivial COVID-19 lesions in CT scans. Our network design achieves a fast execution speed (inference time is 43 ms on a single image) with optimal memory consumption (almost 9 MB). To evaluate the performances of the proposed and state-of-the-art models, we considered two publicly accessible datasets, namely COVID-19-CT-Seg (comprising a total of 3520 images of 20 different patients) and MosMed (including a total of 2049 images of 50 different patients). Results: Our method exhibits average area under the curve (AUC) up to 98.84%, 98.47%, and 95.51% for COVID-19-CT-Seg, MosMed, and cross-dataset, respectively, and outperforms various state-of-the-art methods. Conclusions: These results demonstrate that deep learning-based models are an effective tool for building a robust CAD solution based on CT data in response to present disaster of COVID-19.