By combination of two independent approaches, nuclear resonant inelastic x-ray scattering and firstprinciples calculations in the framework of density functional theory, we demonstrate significant changes in the element-resolved vibrational density of states across the first-order transition from the ferromagnetic low temperature to the paramagnetic high temperature phase of LaFe_13−xSi_x. These changes originate from the itinerant electron metamagnetism associated with Fe and lead to a pronounced magneto-elastic softening despite the large volume decrease at the transition. The increase in lattice entropy associated with the Fe subsystem is significant and contributes cooperatively with the magnetic and electronic entropy changes to the excellent magneto- and barocaloric properties.