The lower hybrid current drive is a potential candidate for sustaining plasma current in tokamak steady state operations, which could be used in China Fusion Engineering Test Reactor (CFETR) with input power up to a few ten megawatts. Such high input power could trigger the well-known parametric instabilities (PIs) at the plasma edge affecting the propagation and absorption of the lower hybrid pump waves, which is studied in this paper. By analyzing the expression of PI growth rates solved from the nonlinear dispersion relation, it is found that the pressure is the key parameter determining the PI characteristics. Ion sound quasi-mode (ISQM) is the dominant decay channel in the low pressure regime, while the ion cyclotron quasi-mode (ICQM), as well as its harmonics, becomes dominant in the intermediate regime. In the high pressure regime, only one mixed channel is found, which is related to Landau damping by free-streaming ions. Analytical expressions of growth rates of these decay channels are also obtained to show the parameter dependences at different pressure limits. The above analytical results are used to estimate the PIs on a typical profile of CFETR, and verified by corresponding numerical calculations. ICQM is found to be the strongest decay channel with a considerable growth rate for CFETR.