A combined generalized spectroscopic ellipsometry measurement and density functional theory calculation analysis is performed to obtain the complete set of infrared active phonon modes in Lu2SiO5 with a monoclinic crystal structure. Two different crystals, each cut perpendicular to a different crystal axis, are investigated. Ellipsometry measurements from 40 to 1200 cm(-1) are used to determine the frequency dependent dielectric function tensor elements. The eigendielectric displacement vector summation approach and the eigendielectric displacement loss vector summation approach, both augmented with anharmonic lattice broadening parameters proposed recently for low-symmetry crystal structures [Mock et al., Phys. Rev. B 95, 165202 (2017)], are applied for our ellipsometry data analysis. All measured and model calculated dielectric function tensor and inverse dielectric function tensor elements match excellently. 23 A(u) symmetry and 22 B-u symmetry infrared active transverse and longitudinal optical modes are found. We also determine the directional limiting modes and the order of the phonon modes within the monoclinic plane. Results from density functional theory and ellipsometry measurements are compared and nearly perfect agreement is observed. We further compare our results to those obtained recently for the monoclinic crystal Y2SiO5, which is isostructural to Lu2SiO5 [Mock et al., Phys. Rev. B 97, 165203 (2018)]. We find that the lattice mode behavior of monoclinic Lu2SiO5 is qualitatively identical with Y2SiO5 and differs only quantitatively. We anticipate that members of the isostructural group of monoclinic symmetry oxyorthosilicates such as Dy2SiO5 or Yb2SiO5 will likely behave very similar in their phonon mode properties as reported here for Lu2SiO5. Published under license by AIP Publishing.