The Lennard-Jones fluid has been considered as a reference model for the analysis of new methodologies. In addition, it can be used as a model for atomic fluids and has been the subject of many numerical studies. In recent years, many works has been carried out to investigate the critical regions of fluids. A common approach has been the use of MC algorithms such as the Gibbs ensemble to obtain the subcritical coexistence data, and then a power law to extrapolate to the critical point. More detailed studies have also been carried out using histogram reweighting methodologies combined with finite size scaling techniques. In the present study, we compare mixed-field theory with finite size scaling with the intersection of the Binder parameter for different system sizes. Furthermore, we propose the use of the “universal” Ising value of the Binder parameter as an estimation of the system-size dependent critical point. The applications of these three methods allows us to estimate the thermodynamic limit critical point. We have calculated the critical point of the pure LJ fluid and a binary mixture selected in order to allow for comparison with previous works. We have obtained excellent agreement between the methodologies confirming the Binder parameter as an interesting method to obtain a high level of accuracy for the critical point location. In addition, the proposed combination of the Binder parameter with finite size scaling techniques is straightforward to apply since it does not require the fitting process of the mixed field theory. The calculation allows also for the calculation of the line of critical points for binary mixtures. Finally, the methodologies have been extended to real binary systems obtaining as well satisfactory results.