  We performed a Raman scattering study of thin films of LiTi$_2$O$_4$ spinel
oxide superconductor. We detected four out of five Raman active modes, with
frequencies in good accordance with our first-principles calculations. Three
T$_{2g}$ modes show a Fano lineshape from 5 K to 295 K, which suggests an
electron-phonon coupling in LiTi$_2$O$_4$. Interestingly, the electron-phonon
coupling shows an anomaly across the negative to positive magnetoresistance
transition at 50 K, which may be due to the unset of other competing orders.
The strength of the electron-phonon interaction estimated from the Allen's
formula and the observed lineshape parameters suggests that the three T$_{2g}$
modes contribute little to superconductivity.
