The present study comprises an investigation involving thermodynamic analysis, microstructural characterisation, and a comparative examination of the solidification sequence in two different aluminium alloys: EN AW 6026 and EN AW 1370. These alloys were modified through the addition of pure indium and a master alloy consisting of indium and bismuth. The aim of this experiment was to evaluate the potential suitability of indium, either alone or in combination with bismuth, as a substitute for toxic lead in free-machining aluminium alloys. Thermodynamic analysis was carried out using Thermo-Calc TCAL-6 software, supplemented by differential scanning calorimetry (DSC) experiments. The microstructure of these modified alloys was characterised using SEM–EDS analysis. The results provide valuable insights into the formation of different phases and eutectics within the alloys studied. The results represent an important contribution to the development of innovative, lead-free aluminium alloys suitable for machining processes, especially for use in automatic CNC cutting machines. One of the most important findings of this research is the promising suitability of indium as a viable alternative to lead. This potential stems from indium’s ability to avoid interactions with other alloying elements and its tendency to solidify as homogeneously distributed particles with a low melting point. In contrast, the addition of bismuth does not improve the machinability of magnesium-containing aluminium alloys. This is primarily due to their interaction, which leads to the formation of the Mg3Bi2 phase, which solidifies as a eutectic with a high melting point. Consequently, the presence of bismuth appears to have a detrimental effect on the machining properties of the alloy when magnesium is present in the composition.