We have performed micro Raman measurements on LiBH4 and LiBD4 powders for temperatures between 5 and 300 K. At the lowest temperature, the peak energies agree very well with the results of a calculation within the density functional theory for the orthorhombic structure. The spectra are dominated by three separated bands: the external modes, the internal bending, and the internal stretching vibrations. Internal refers to vibrations within the BH4 tetrahedrons, whereas external modes imply motions of Li and BH4. The temperature dependence of the observed phonons corroborates the strong anharmonicity of the system. Due to the anharmonicity, Fermi resonances occur between the first order stretching modes and the second order bending modes of LiBH4. Moreover, the linewidths of the observed modes in LiBH4 have an Arrhenius-like component, with activation energies ranging from 250 to 500 K.