We have studied the diagonal and off-diagonal optical conductivity of a LuFe2 single crystal grown by the flux method. Using spectroscopic ellipsometry we have measured the dielectric function from 1.5 to 5.5 eV. The magneto-optical parameters (Kerr rotation and ellipticity) from 1.4 to 4.0 eV were obtained using a magneto-optical polar Kerr spectrometer at temperatures between 7 and 295 K and applied magnetic fields up to 1.2 T which fully saturates the magnetic moment of LuFe2. We describe the apparatus and evaluate the off-diagonal conductivity components from the data. Theoretical calculations of optical conductivities and magneto-optical parameters were performed using the tight binding-linear muffin tin orbitals method within the local spin density approximation. When lifetime broadening is included, the calculations agree well with the experimental data.