The design of the first lattice light-sheet microscope equipped with incoherent holographic detection for neuronal imaging is presented. The device is designed for the capture of 3-D complex amplitude images moving neither the sample stage nor the detection microscope objective. The system is built onto a conventional lattice light-sheet (LLS) microscope, as a second detection arm, equipped with an incoherent holographic optical design and a monochromatic CMOS sensor. The compact system could be mounted on any lattice light-sheet and light sheet instruments due to flexibility of changing the numerical aperture of the excitation light by changing the anulus of the diffraction mask. For this study, fluorescence imaging is supported by illumination at 488 nm. This work relies upon the use of the self-interference property of the emitted fluorescent light, in which three or four Fresnel patterns are projected onto samples to create interference patterns of a 3-D object using a phase shifting technique. The projection of the diffraction patterns of samples is achieved with a spatial light modulator which allows single (IHLLS 1L) or dual lens (IHLLS 2L) patterns superposition with randomly selected pixels. The focal lengths of the lenses are calculated in two steps using OpticStudio (Zemax, LLC) design to provide the optimal compromise between the two requirements for magnification and dual-beam size matching at the camera plan on the one hand and space between the objective and camera on the other. We used the IHLLS-1L for calibration purposes and IHLLS-2L for recording sample holograms. The system allows the generation of high-resolution amplitude and phase images with larger scanning area and depth of field than the original LLS. Neuronal 3-D maps are built from sets of images acquired at various z-sections, determined by galvanometric mirror depth positions in the sample. This paper describes the concept of the instrument and details its optical design. This paper briefly describes the concept of the instrument and details its optical design. An overview of the key performances is also provided.