In order to explain the results of the non-inductive current produced in the lower hybrid current drive (LHCD) experiments, a broadening of the radiofrequency (RF) power spectrum coupled to tokamak plasma is necessary to occur. The presented modelling, supported by diagnostic measurements, shows that the parametric instability (PI) driven by ion sound quasimodes that occur in the scrape-off plasma layer located near to the launcher mouth, produces a significant broadening of the launched LH spectrum. Considering the parameters of LHCD experiments of JET (Joint European Torus), and other machines as well, the PI growth rate is high enough for producing the compensation of the convective losses and, consequently, the broadening of a small fraction (10%) of the launched power spectrum. Such phenomenon is identified to be intrinsic of the RF power coupling in the LHCD experiments. As principal implication of considering such spectral broadening in modelling the LH deposition profile, experiments able evidencing the effects of a well-defined LH deposition profile, like those with LHCD-sustained internal transport barriers of JET, were successfully interpreted. The present work is important for addressing the long-lasting debate on the problem of the so-called spectral gap in LHCD. The design of LHCD scenarios relevant to the modern fusion research program, which require the control of the plasma current profile in the outer half of plasma, can be properly achieved by considering the PI-induced spectral broadening.