We present a combined experimental and theoretical analysis of the dielectric and vibrational properties of crystalline lutetium oxide in its ground-state bixbyite structure. The vibrational dielectric function of L u 2 O 3 thin films grown by atomic-layer deposition was studied by infrared transmission and reflection-absorption spectroscopies, selectively accessing transverse and longitudinal optical frequencies. The static dielectric constant is extracted analyzing the infrared response. We also present first-principles density-functional linear-response calculations, which are in close agreement with experiment, and provide insight into the microscopic nature of vibrational spectra and dielectric properties.