By incorporating parametric instabilities of lower hybrid (LH) waves into a ray-tracing Fokker-Planck code, accurate simulations of the LH deposition profiles are provided, which are useful for interpreting the long-lasting internal transport barriers (ITBs) sustained by lower hybrid current drive (LHCD) on JET (Joint European Torus). Utilizing the new model, the simulation of the q-profile evolution results in agreement with that provided by the motional Stark effect reconstructed equilibria. Low magnetic shear (sapproximate to0) is produced by LHCD in a layer close to the ITB radial foot.