The phonon dispersion was measured at room temperature (above the Néel temperature T_N) along (0,0,L) in the tetragonal phase of LaFeAsO using inelastic x-ray scattering. Magnetostructural effects are well documented in the AFe₂As₂-based (A = Ca, Sr, Ba, Eu) systems. Only recently have single crystals of LaFeAsO become available. The experimentally observed splitting between two A_1g phonon modes at 22 and 26 meV is only reproduced in spin-polarized calculations. Magnetostructural effects similar to those observed in the AFe₂As₂ materials are confirmed to be present in LaFeAsO. This is discussed in terms of the strong antiferromagnetic correlations that are known to persist above T_N and into the tetragonal phase.