The frequency spectral broadening of lower hybrid (LH) waves injected into tokamak plasmas is extensively analysed with reference mostly to experimental data from the ASDEX tokamak. The link between the magnitude of the pump spectral width and the degradation of the LH current drive efficiency (up to a factor of 2), pointed out in previous works, is explained. The experimental behaviour of LH power absorption is also well reproduced, even in situations when the access of the launched LH waves to the core plasma should be largely forbidden. Experiments are described that are aimed at determining whether parametric decay instabilities (PDIs) or scattering of LH waves by density fluctuations in the plasma edge are causes of the broadening of the LH pump frequency spectrum. Fluctuations emerge as the largely dominant process, while no signature of PDI processes is observed. Careful measurements of the density fluctuations in the ASDEX scrape-off layer plasma allow the analytical description given by Andrews and Perkins (1983) to be assumed as the appropriate model for LH scattering. Indeed, it supplies the correct magnitude for the frequency spectral width of the LH pump, and explains quantitatively, together with a ray tracing code, why the CD efficiency decreases with the broadening of the pump spectrum. It can also account for the observed LH power absorption coefficient