Temperature-dependent FAR-infrared reflectivity spectra of partially ordered magnetodielectric La2CoMnO6 is presented, from room temperature up to 675 K. A clear first-ordered structural phase transition (SPT) from a monoclinic structure with 2 1 / symmetry to a rhombohedral phase with 3 ̅ symmetry was evidenced from the behaviour of polar phonon modes at TC ~ 590 K. The temperature dependences of the transversal and longitudinal phonon branches, dielectric strengths, and damping of the strongest dielectric modes confirm the significant contribution of the phonon modes on the SPT, and revealed an important lattice anharmonicity, particularly for the low frequency modes. In addition, these investigations showed that structural ordering does not inhibit the SPT, and provided valuable information towards the polar phonons, their implications on intrinsic dielectric constant in double perovskites and in related compounds.