In the experimental characterization of the nonlinear optical properties of dye-doped liquid crystals by the Z-scan technique with CW lasers it is rather common to assign it a Kerr or thermal nonlinear response. In this work, we demonstrate that neither of them correctly describes all features of the Z-scan obtained in planar samples of methyl red doped 5CB liquid crystal using He-Ne CW illumination, where a strong nonlinear optical response is observed. The Z-scan curves depend strongly on the input polarization of the beam obtaining negative and positive nonlinear response for polarizations parallel and orthogonal to the director vector. We discuss and compare the effect of an additional incoherent linearly-polarized beam and plain heating source on Z-scan experiments. A theoretical model, valid for small and large phase modulation, is proposed based on the assumption that the sample can be considered as a thin lens with a photoinduced focal length dependent on the Gaussian beam radius m (where m is an integer), obtaining good agreement with the experimental curves for m=3, which is neither a Kerr nor thermal nonlinearity.