In this study, L. essential oil (CEO) and L. essential oil (MEO) was steam-distillated under reduced pressure. We henceforth obtained three fractions for each essential oil: CF, CF, CF, MF, MF, and MF. Then, these fractions were characterized using the gas chromatography-mass spectrometry (GC-MS) technique. The results indicated that some fractions were rich in oxygenated compounds (i.e., CF, CF, MF and MF) with concentrations ranging from 79.21% to 98.56%. Therefore, the influence of the chemical composition of the essential oils on their antifungal activity was studied. For this purpose, three food spoilage fungi were isolated, identified, and inoculated in vitro, in order to measure the antifungal activity of CEO, MEO, and their fractions. The results showed that stronger fungi growth inhibitions (FGI) (above 95%) were found in fractions with higher percentages of oxygenated compounds, especially with (-)-carvone and terpin-4-ol as the major components. Firstly, this work reveals that the free-terpenes hydrocarbons fractions obtained from MEO present higher antifungal activity than the raw essential oil against two families of fungi. Then, it suggests that the isolation of (-)-carvone (97.15 ± 5.97%) from CEO via vacuum distillation can be employed successfully to improve antifungal activity by killing fungi (FGI = 100%). This study highlights that separation under reduced pressure is a simple green method to obtain fractions or to isolate compounds with higher biological activity useful for pharmaceutical products or natural additives in formulations.