In this paper, we present the temperature-dependent far-infrared reflectivity spectra of partially ordered magnetodielectric La2CoMnO6 from room temperature to 673 K. We demonstrate a clear first-order structural phase transition (SPT) from a monoclinic structure with P21/n symmetry to a rhombohedral phase with R3¯ symmetry from the behavior of the polar phonon modes at TC ∼ 590 K. The temperature-dependent transversal and longitudinal phonon branches, dielectric strengths, and damping of the strongest dielectric modes support the significant contribution of the phonon modes to the SPT and reveal an important lattice anharmonicity, especially for the low-frequency modes. Also, these investigations showed that structural ordering does not inhibit the SPT and provided valuable information regarding the polar phonons and their effects on the intrinsic dielectric constant in double perovskites and related compounds.