Lattice light sheet microscopy is uniquely positioned in biomedical imaging modalities due to its superior performance in temporal-spatial resolution and low phototoxicity. However, the imaging system is commonly complicated because producing lattice light sheets involves mechanical scanning and precise alignment. In this Letter, we present an experimental scheme for motionless synthesis and scanning of lattice light sheets using a single digital micromirror device. By fully exploiting its ability of complex amplitude modulation and fast switching, single-shot construction of a uniform lattice light sheet can be achieved by digital dithering. In particular, fast scanning of the lattice light sheet in the depth direction is also realized without any mechanical motion. As a proof of concept, various lattice light sheets are generated and characterized in the experiments. Our work is expected to benefit the development of a compact and low-price lattice light-sheet microscope for biomedical imaging.