The phonon dispersion was measured at room temperature along (0,0,L) in the tetragonal phase of LaFeAsO using inelastic x-ray scattering. Spin-polarized first-principles calculations imposing various types of antiferromagnetic order are in better agreement with the experimental results than nonmagnetic calculations, although the measurements were made well above the magnetic ordering temperature, TN. Splitting observed between two A1g phonon modes at 22 and 26 meV is only reproduced in spin-polarized calculations. Magnetostructural effects similar to those observed in the AFe2As2 (A=Ca,Sr,Ba,Eu) materials are present in LaFeAsO. The inclusion of Fe spin is necessary to find reasonable agreement of the calculations with the measured spectrum well above TN. On-site Fe and As force constants show significant softening compared to nonmagnetic calculations, however an investigation of the real-space force constants associates the magnetoelastic coupling with a complex renormalization instead of softening of a specific pairwise force.