A thorough analysis of the first-order vibrational spectrum of LuVO4 is presented by using polarized micro-Raman spectroscopy with special focus on the phonon modes with the weakest intensity and occasional controversial assignment. Group-theory analysis is carried out to demonstrate the determination of numbers and symmetries of the Raman active modes. Crystal- and correlation-field splitting effects in the vibrational spectrum of LuVO4 are discussed. Under conditions adjusted to minimize the birefringence effects we recorded, in each main scattering configuration, a series of Raman spectra in different sample orientations achieved by rotating the sample around the incident laser beam. The dependence of the Raman intensity on the rotational angle allowed us to identify the correct symmetry of the phonons with exceptionally weak scattering cross-section. A complete assignment of all twelve first-order Raman active phonons of LuVO4 is thus obtained.