The lattice structure of invar-alloy offers the advantages of low thermal expansion coefficient and low density, thus rendering it extremely suitable for the aerospace industry. Selective laser melting (SLM), also known as laser powder bed fusion (L-PBF), is the most widely used metal additive-manufacturing technology and offers significant advantages in manufacturing complex lattice structures. However, our current understanding regarding factors that affect the performance of invar-alloy lattice structures fabricated via SLM is inadequate. Hence, a three-factor, three-level orthogonal experimental design was employed to optimize the SLM process parameters of invar-alloy. Using tensile strength and yield strength as indicators, we propose the following optimal parameters: laser power, 280 W; scanning speed, 1000 mm/s; and scanning spacing, 0.12 mm. Tensile samples prepared under these parameters indicate yield and tensile strengths of 340 MPa and 419 MPa, respectively. Based on the optimized parameters, we investigated the effect of scanning speed on the geometric and mechanical properties of the invar-alloy lattice structure fabricated via SLM. The result shows that the lattice structure fabricated under a laser power of 280 W, a scanning speed of 1000 mm/s, and a scanning spacing of 0.12 mm exhibits both favorable mechanical and geometric performances.