Composite lattice anisogrid adapters are highly favored in space rocketry design, serving as crucial interface structures between rocket stages or between the payload and its supporting structure. Their unique structural configuration allows them to withstand significant weight loads without succumbing to buckling. However, optimizing their design parameters could further enhance their strength and efficiency. Particularly, reinforcing the lower hoop ribs in a conical lattice adapter can substantially enhance its strength under axial compressive loads, thus preventing buckling. In this study, we begin by presenting a finite-element model of a lattice adapter featuring helical ribs that follow geodesic paths. To validate the model's accuracy, experimental prototypes and finite-element models from previous research are utilized. Subsequently, a neural network model is trained using the dataset generated from finite-element analysis results. This neural network model aims to predict, explore, and optimize the impact of lower hoop ribs' thicknesses on the critical axial buckling load of the adapter. The analysis ultimately confirms that an adapter designed with optimized ribs demonstrates a remarkable 51% increase in load capacity before buckling compared to an adapter designed with uniform ribs. This underscores the significance of optimizing design parameters for enhancing structural performance in space rocketry applications.