We present a detailed theoretical and numerical analysis on the temporal-spectral-spatial evolution of a high-peak-power femtosecond laser pulse in two sets of systems: a pure lithium niobate (LN) plate and a periodically poled lithium niobate (PPLN) plate. We develop a modified unidimensional pulse propagation model that considers all the prominent linear and nonlinear processes and carried out the simulation process based on an improved split-step Fourier transformation method. We theoretically analyze the synergic action of the linear dispersion effect, the second-order nonlinearity (2nd-NL) second-harmonic generation (SHG) effect, and the third-order nonlinearity (3rd-NL) self-phase modulation (SPM) effect, and clarify the physical mechanism underlying the peculiar and diverse spectral broadening patterns previously reported in LN and PPLN thin plate experiments. Such analysis and discussion provides a deeper insight into the synergetic contribution of these linear and nonlinear effects brought about by the interaction of a femtosecond laser pulse with the LN nonlinear crystal and helps to draw a picture to fully understand these fruitful optical physical processes, phenomena, and laws.