Pressure-induced vibrational and superconducting properties of lanthanum hydrides (LaH₂ and LaH₃) have been studied using first principles calculations. It is found that LaH₂ and LaH₃ are dynamically stable in the pressure ranges of 0–39 GPa and 4–35 GPa, respectively. The character of phonon dispersion curves for LaH₂ and LaH₃ is analyzed under pressure. The zone-center phonon mode eigen displacements that represent infrared and Raman activity are also obtained, which are essential to the analysis of spectral experiments. The calculations based on Bardeen–Cooper–Schrieffer theory indicate that LaH₂ almost has no superconducting behavior even under pressure, in reasonable agreement with previous theoretical calculations and experiments. Whereas, LaH₃ presents a considerable high superconducting transition temperature (T_c) at the onset of the face centered cubic structure, while it decreases exponentially under further compression up to 25 GPa and finally almost approaches zero. Further analysis indicates that the underlying mechanism of these two distinct superconducting behaviors are closely related to the hybridization between the H_O-s state and La-d state. The mode Grüneisen parameters of two hydrides are also analyzed under 35 GPa, finding that the hydrogen atoms at octahedral sites are responsible for the superconducting properties of LaH₃, and in fact, the unobserved superconducting behavior in LaH₂ can be interpreted as the absence of hydrogen at octahedral sites compared with LaH₃.