This study explores how variations in the transverse spoke thickness of honeycomb non-pneumatic tires (NPTs) influence their lateral stiffness. The NPT model was uniformly segmented along the width direction, with distinct thickness gradients assigned to the spokes to analyze their effect on lateral stiffness. Latin hypercube sampling approach was implemented to develop a set of samples that could analyze the impact of variations in the thickness of spokes on tire stiffness. High lateral rigidity in honeycomb NPTs often compromises vehicle handling stability, highlighting the necessity of optimizing lateral stiffness. Based on the generated sample points, two surrogate models—response surface model (RSM) and radial basis function model (RBF)—were constructed and employed as the basis for optimization using the non-dominated sorting genetic algorithm (NSGA-II). The final outcome delivered a set of Pareto optimal solutions with minimized lateral rigidity and compared the results to the initial NPT-1 model. The findings indicated significant reductions in lateral stiffness for optimized NPTs, with the initial stiffness of 449.17 N/mm decreasing to 410.44 N/mm and 410.95 N/mm for NPT-OPRSM and NPT-OPRBF, respectively. These reductions, approximately 8.63%, and 8.51%, significantly enhanced vehicle handling performance. Additionally, the refined NPTs demonstrated good performances in lateral stiffness, weight reduction, and peak stress endurance of the spokes.