We investigate the role of atomic distortions in non-relativistic spin splitting in perovskite oxides with Pbnm symmetry. Using LaMnO3 as a representative material, we analyze its non-relativistic spin splitting through a combined phonon and multipolar analysis. Our study provides key insights into how structural distortions and magnetic ordering drive ferroically ordered magnetic multipoles, which, in turn, give rise to non-relativistic spin splitting. Based on these findings, we propose three strategies for engineering non-relativistic spin splitting: modifying the A-site cation size, strain engineering, and electric field control in superlattice structures. Our work establishes a framework for designing non-relativistic spin splitting in the Brillouin zone of oxide perovskites.