This study addresses numerical modeling and time-domain simulations of the lowering operation for installation of an offshore wind turbine monopile (MP) with a diameter of 5.7 m and examines the nonstationary dynamic responses of the lifting system in irregular waves. Due to the time-varying properties of the system and the resulting nonstationary dynamic responses, numerical simulation of the entire lowering process is challenging to model. For slender structures, strip theory is usually applied to calculate the excitation forces based on Morison's formula with changing draft. However, this method neglects the potential damping of the structure and may overestimate the responses even in relatively long waves. Correct damping is particularly important for the resonance motions of the lifting system. On the other hand, although the traditional panel method takes care of the diffraction and radiation, it is based on steady-state condition and is not valid in the nonstationary situation, as in this case in which the monopile is lowered continuously. Therefore, this paper has two objectives. The first objective is to examine the importance of the diffraction and radiation of the monopile in the current lifting model. The second objective is to develop a new approach to address this behavior more accurately. Based on the strip theory and Morison's formula, the proposed method accounts for the radiation damping of the structure during the lowering process in the time-domain. Comparative studies between different methods are presented, and the differences in response using two types of installation vessel in the numerical model are also investigated.