Wavelength-resolved neutron tomography (WRNT) is an emerging technique for characterizing samples relevant to the materials sciences in 3D. WRNT studies can be carried out at beam lines in spallation neutron or reactor-based user facilities. Because of the limited availability of experimental time, potential imperfections in the neutron source, or constraints placed on the acquisition time by the type of sample, the data can be extremely noisy resulting in tomographic reconstructions with significant artifacts when standard reconstruction algorithms are used. Furthermore, making a full tomographic measurement even with a low signal-to-noise ratio can take several days, resulting in a long wait time before the user can receive feedback from the experiment when traditional acquisition protocols are used. In this paper, we propose an interlaced scanning technique and combine it with a model-based image reconstruction algorithm to produce high-quality WRNT reconstructions concurrent with the measurements being made. The interlaced scan is designed to acquire data so that successive measurements are more diverse in contrast to typical sequential scanning protocols. The model-based reconstruction algorithm combines a data-fidelity term with a regularization term to formulate the wavelength-resolved reconstruction as minimizing a high-dimensional cost-function. Using an experimental dataset of a magnetite sample acquired over a span of about two days, we demonstrate that our technique can produce high-quality reconstructions even during the experiment compared to traditional acquisition and reconstruction techniques. In summary, the combination of the proposed acquisition strategy with an advanced reconstruction algorithm provides a novel guideline for designing WRNT systems at user facilities.