In this paper, the operational forecasts of the rapid intensification (RI) of Typhoon Lekima (1909) by the Tropical Regional Atmosphere Model for the South China Sea of China Meteorological Administration (CMA-TRAMS) and the high-resolution products of the ECMWF atmospheric model （HRES） are analyzed. Numerical sensitivity experiments are designed and carried out from the perspectives of horizontal resolution, initial and boundary conditions, and physical parameterization schemes. It is found that CMA-TRAMS and HRES both can predict the strengthening of Tyhpoon Lekima to some extent, but the predicted strengthening speed is obviously lower than observation. The two models both fail to meet the 24 h and 12 h RI standards, but can reach the 6 h RI standard. The experiment using 3 km horizontal resolution produces better forecasts of track and intensity of Lekima than that using 9 km resolution based on CMA-TRAMS, but it cannot improve the RI forecast. Nevertheless, the prediction of typhoon RI is significantly improved if the scheme has 3 km resolution nested to 9 km resolution. The experiment using the MRF boundary layer parameterization scheme generally performs better in forecasting typhoon track, intensity and RI than that using the YSU scheme. When the initial and boundary conditions with higher vertical resolution are used, combined with the sea surface temperature (SST) parameterization scheme, the RI forecast is obviously improved in the frequency and maximum speed. Analyses indicate that the SST parameterization scheme increases the difference between sea and air temperature, affecting the heat transport and exchange significantly. The enhancement of sensible heat flux from the ocean to the atmosphere and the enhancement of latent heat flux in the inner-core section of typhoon increase the temperature and humidity and magnify the negative tendency of pressure.