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Under consideration is a modified Toda lattice system with a perturbation parameter, which may describe the particle motion in a lattice. With the aid of symbolic computation Maple, the discrete generalized (m , 2 N − m) -fold Darboux transformation (DT) of this system is constructed for the first time. Different types of exact solutions are derived by applying the resulting DT through choosing different m. Specifically, standard soliton solutions, rational solutions and their mixed solutions are given via the (2 N , 0) -fold DT, (1 , 2 N − 1) -fold DT and (2 , 2 N − 2) -fold DT, respectively. Limit states of various exact solutions are analyzed via the asymptotic analysis technique. Compared with the known results, we find that the asymptotic states of mixed solutions of standard soliton and rational solutions are consistent with the asymptotic analysis results of solitons and rational solutions alone. Soliton interaction and propagation phenomena are shown graphically. Numerical simulations are used to explore relevant soliton dynamical behaviors. These results and properties might be helpful for understanding lattice dynamics. [ABSTRACT FROM AUTHOR]