Phase stabilities in the La2O3-P2O5 pseudobinary system have been theoretically analyzed. Phonon modes of five crystals, i.e., La2O3, La3PO7, LaPO4, LaP3O9, and LaP5O14, and vibrational modes of gaseous P2O5(g) are computed from first principles in order to obtain the contribution of vibrations to the free energy. Additional dynamical contributions, i.e., rotations and translations are also taken into account for the gaseous P2O5(g). Vibrational states strongly reflect the crystal structures and bonding states. In this system, the strong P-O covalent bonds in PO4 units and the relatively weak La-O bonds are found to be the key factors determining the vibrational spectra. In the oxyphosphate, La3PO7, the two bonding states are coexisting, and the vibrational spectrum is approximately an average of La2O3 and LaPO4. On the other hand, the P2O5-rich compounds, i.e., LaP3O9 and LaP5O14, cannot be treated in the same manner. Their PO4 units form corner-sharing networks whose vibrations are strongly correlated. The networks raise the vibrational frequencies, leading to high-frequency modes up to 40 THz. The Gibbs energies using the calculated vibrational spectra are in reasonable agreement with the available data of La2O3, LaPO4, and P2O5(g), e.g., the differences between the calculated and reported values are less than 2 kJ/mol-atom (20 meV/atom) at 1500 K. The Gibbs energies and the phase stabilities of the other three compounds, La3PO7, LaP3O9, and LaP5O14, are evaluated, whose data are yet unknown so far.