We report two-phase Monte Carlo simulations of the liquid-vapor interface of the Lennard-Jones (LJ) fluids in order to study the impact of the methodology used for the energy calculation on the oscillatory behavior of the surface tension with the system sizes. The surface tension values are illustrated through the LJ parameters of methane. The first methodology uses a standard truncated LJ potential, the second one adds a long range correction (LRC) contribution to the energy into the Metropolis scheme, and the third one uses a LJ potential modified by a polynomial function in order to remove the discontinuities at the cutoff distance. The surface tension is calculated from the mechanical and thermodynamic routes and the LRCs to the surface tension are systematically calculated from appropriate expressions within these definitions. The oscillatory behavior has been studied as a function of the size of the interfacial area and of the length of the dimension perpendicular to the surface. We show that the methodology has an important effect on the oscillatory variation in the surface tension with the system size. This oscillatory variation in the surface tension with the system size is investigated through its intrinsic and LRC contributions. We complete this work by studying the dependence of the surface tension with respect to the cutoff distance when the LRC part to the energy is considered into the Metropolis scheme.