Diffuse optical tomography (DOT) leverages near-infrared light propagation through tissue to assess its optical properties and identify abnormalities. DOT image reconstruction is an ill-posed problem due to the highly scattered photons in the medium and the smaller number of measurements compared to the number of unknowns. Limited-angle DOT reduces probe complexity at the cost of increased reconstruction complexity. Reconstructions are thus commonly marred by artifacts and, as a result, it is difficult to obtain an accurate reconstruction of target objects, e.g., malignant lesions. Reconstruction does not always ensure good localization of small lesions. Furthermore, conventional optimization-based reconstruction methods are computationally expensive, rendering them too slow for real-time imaging applications. Our goal is to develop a fast and accurate image reconstruction method using deep learning, where multitask learning ensures accurate lesion localization in addition to improved reconstruction. We apply spatial-wise attention and a distance transform based loss function in a novel multitask learning formulation to improve localization and reconstruction compared to single-task optimized methods. Given the scarcity of real-world sensor-image pairs required for training supervised deep learning models, we leverage physics-based simulation to generate synthetic datasets and use a transfer learning module to align the sensor domain distribution between in silico and real-world data, while taking advantage of cross-domain learning. Applying our method, we find that we can reconstruct and localize lesions faithfully while allowing real-time reconstruction. We also demonstrate that the present algorithm can reconstruct multiple cancer lesions. The results demonstrate that multitask learning provides sharper and more accurate reconstruction.