This paper reports the first experimental observation of phonons and their softening on single crystalline LaPt₂Si₂ via inelastic neutron scattering. From the temperature dependence of the phonon frequency in close proximity to the charge density wave (CDW) q-vector, we obtain a CDW transition temperature of T_CDW = 230 K and a critical exponent β = 0.28 ± 0.03. This value is suggestive of a non-conventional critical behavior for the CDW phase transition in LaPt₂Si₂, compatible with a scenario of CDW discommensuration (DC). The DC would be caused by the existence of two CDWs in this material, propagating separately in the non equivalent (Si1–Pt2–Si1) and (Pt1–Si2–Pt1) layers, respectively, with transition temperatures T_CDW−1 = 230 K and T_CDW−2 = 110 K. A strong q-dependence of the electron-phonon coupling has been identified as the driving mechanism for the CDW transition at T_CDW−1 = 230 K while a CDW with 3-dimensional character, and Fermi surface quasi-nesting as a driving mechanism, is suggested for the transition at T_CDW−2 = 110 K. Our results clarify some aspects of the CDW transition in LaPt₂Si₂ which have been so far misinterpreted by both theoretical predictions and experimental observations and give direct insight into its actual temperature dependence.