Digital tomosynthesis systems promise better image quality compared to radiography, and thus these have been widely used in chest, dental, and breast imaging. Currently, two acquisition modes are used in digital tomosynthesis systems, such as step-and-shoot mode and continuous mode. The main difference between two acquisition modes is x-ray tube motion during data scanning, which affects spatial resolution and contrast. In this work, we investigate the effects of the X-ray tube motion on lesion detectability with anatomical background. We considered six spherical objects with diameters of 0.5, 0.8, 1, 2, 5, 10 mm as lesions, and anatomical background was modeled using the power law spectrum of breast anatomy. Projection data were acquired using two acquisition modes, and in-plane images are reconstructed using Feldkamp-Davis-Kress (FDK) algorithm. To show the effect of x-ray tube motion on lesion detectability, we computed task signal-to-noise ratio (SNR) of channelized Hotelling observer with Laguerre-Gauss channels for six spherical objects. Our results show that the task-SNR of step-and-shoot mode is higher than that of continuous mode for small lesion sizes (i.e., less than 1 mm diameter). This behavior indicates that tomosynthesis system with step-and-shoot mode is more beneficial to improve the detectability of small lesions than that with continuous mode.