This study investigates the optimization of Laser Powder Bed Fusion (LPBF) process parameters to enhance the mechanical properties of the Russian Ni superalloy VZh159 (a close analogue of IN718) material that is commonly used in critical aerospace applications, and the corresponding studies of the grain structure within and near the melt pool formed by a single laser scan line. Through a factorial experimental approach, the influence of laser power and scanning speed on the tensile strength, yield strength, and ductility was determined. Metallurgically sound samples (based on hydrostatic weighing data and microscopy, with practically no pores detected) were obtained with nine combinations of power and scanning speed, showing significant variation in the tensile strength (in the 1,040–1,220 MPa range) and yield strength (in the 560–1,100 MPa range), which correlated with the cross-sectional area of the single scan line (for example, the depth of the melt pool varied in the range 410–530 µm), while the average grain size (deduced from Electron Backscatter Diffraction (EBSD) images) remained statistically unchanged. Key findings indicate that the optimal LPBF parameters are a laser power of 250 W, a scanning speed of 600 mm/s, and a hatch distance of 0.12 mm, which together yield the best combination of high tensile strength and ductility. This study provides new insights into the effects of LPBF parameters on the microstructure, particularly the formation of the γ′ strengthening phase and its correlation with mechanical performance. The research addresses a critical gap in understanding the relationship between LPBF processing conditions and the resulting microstructural and mechanical properties, offering potential improvements in manufacturing efficiency and material performance.