The proposed work presents a model to understand the lower hybrid turbulence as observed by the Magnetospheric Multiscale (MMS) mission in the magnetic reconnection regions of magnetopause by the energetic electron beams (generated by the magnetic reconnection process). The magnetic reconnection process has been substituted by the “energetic electron beam source” in this model. Therefore, in the proposed model, dynamical equations for beam-driven lower hybrid wave (LHW) have been formulated, foreseeing that it will evolve from noise level and then attain large amplitude due to beam energy. At large amplitude, non-linear effects due to ponderomotive force dominate, causing LHW localization and the turbulent state. A non-linear two-dimensional model with the help of the two-fluid dynamics has been developed. The present mathematical model considers the interaction between pump LHW and low frequency magnetosonic wave (MSW). The MSW, present in the background, has been contemplated as the source of density perturbations in LHW dynamics. The LHW is the source of ponderomotive nonlinearity in the medium and is incorporated in the MSW wave dynamics. With the help of the growth term associated with the electron beam, dynamical equations for LHW and MSW have been established. The two coupled equations, thus obtained, were solved with the help of numerical simulation techniques. The results show the temporal evolution of the LHW from noise level and formation of localized structures and turbulence consistent with MMS mission observations.