Laser Peening (LP) is a surface modification technology that can induce high residual stresses in a metallic material. The relation between LP process parameters, in particular laser sequences, as well as pulse parameters and the resulting residual stress state was investigated in this study. The residual stress measurements, performed with the hole drilling technique, showed a non-equibiaxial stress profile in laser peened AA2024-T3 samples with a clad layer for certain parameter combinations. Shot overlap and applied energy density were found to be crucial parameters for the characteristic of the observed non-equibiaxial residual stress profile. Furthermore, the investigation showed the importance of the advancing direction, as the advancing direction influences the direction of the higher compressive residual stress component. The direction of higher residual stresses was parallel or orthogonal to the rolling direction of the material. The effect was correlated to the microstructural observation obtained via electron backscattered diffraction. Additionally, for peening with two sequences of different advancing directions, the study showed that the order of applied advancing directions was important for the non-equibiaxiality of the resulting residual stress profile.