In this study, a design optimization framework is presented that utilizes the topology and lattice structure optimization approaches to design an aerospace component for additive manufacturing (AM). In this framework, the topology optimization is first utilized to find the relative density distribution in the design space of the component that maximizes its stiffness under the volume and strength constraints. The optimized density distribution is used to generate an initial lattice structure topology. A two-step size optimization is also carried out using the beam element formulation in the FEA. The diameters of the strut members in the lattice structure are aimed to be kept within the manufacturability limits of the selective laser melting (SLM) process with AlSi10Mg alloy to satisfy the volume and stress constraints while maximizing the overall stiffness. Optimized designs are determined with four different lattice types. The best design among them is analyzed to ensure an additional natural frequency constraint using modal analysis. Thus, a novel lattice structure design is achieved that satisfies the strength and vibration-specific requirements of the aerospace component for a real-world application. The developed lattice structure design of the aerospace component is achieved with a 30% reduction in weight while still satisfying the desired requirements compared to the existing design in use. The presented lattice design optimization framework is presented in a way that is not application-specific so that it can also be used for the design of different components for AM. The future work includes experimental validation of the strength and vibration performances of the SLM-fabricated design.