The Leighton dish formerly at the Caltech Submillimeter Observatory will be reassembled to become the Leighton Chajnantor Telescope (LCT). It will be required to demonstrate high surface accuracy and controlled radiation patterns at high frequency, which are largely limited by surface error due to panel misalignment on the primary reflector. Not only the surface rms error but also the error distribution has effect on the radiation pattern of the antenna. Therefore, analyzing the effect of error distributions resulting from various panel misalignments on the radiation pattern of the antenna will facilitate better compensation of surface errors during the reassembly process. To acquire the radiation pattern of LCT's antenna with panel misalignments, we first propose a simulation method based on physical optics and the physical theory of diffraction, which offers precise results but is time-consuming, especially at high frequencies. Then, we propose a rapid computation method that combines the method of calculating the optical path difference (OPD), the OPD fitting method, and the aperture integration method for segmented reflectors. Experimental results demonstrate that the rapid computation method is highly efficient and accurate compared to the simulation method. In order to show the effect of error distributions due to two typical panel misalignments (i.e., piston and tip-tilt) on radiation patterns, experiments are conducted using the two proposed methods for various error distributions. These experiments indicate that for the same surface rms error, smaller panel errors at smaller normalized aperture radii are more conducive to achieving improved characteristics of the radiation patterns, such as reduced peak gain losses and lower sidelobe levels. Additionally, comparison experiments also reveal that variations in piston error have a greater impact on the radiation patterns than variations in tip-tilt error under the same surface rms error.