Amaranthus hypochondriacus is a source of molecules with reported health benefits such as antioxidant activity and cancer prevention. The objective of this research was to optimize the conditions for preparing a liposome formulation using amaranth unsaponifiable matter as a source of squalene in order to minimize the particle size and to maximize the encapsulation efficiency of liposomes for carrying and delivering soybean lunasin into melanoma cell lines. Amaranth oil was extracted using supercritical dioxide carbon extraction (55.2 MPa pressure, 80 °C temperature, solvent (CO2)-to-feed (oil) ratio of 20). The extracted oil from amaranth was used to obtain the unsaponifiable enriched content of squalene, which was incorporated into liposomes. A Box–Behnken response surface methodology design was used to optimize the liposome formulation containing the unsaponifiable matter, once liposomes were optimized. Soybean lunasin was loaded into the liposomes and tested on A-375 and B16-F10 melanoma cells. The squalene concentration in the extracted oil was 36.64 ± 0.64 g/ 100 g of oil. The particle size in liposomes was between 115.8 and 163.1 nm; the squalene encapsulation efficiency ranged from 33.14% to 76.08%. The optimized liposome formulation contained 15.27 mg of phospholipids and 1.1 mg of unsaponifiable matter. Cell viability was affected by the liposome formulation with a half-maximum inhibitory concentration (IC50) equivalent to 225 μM in B16-F10 and 215 μM in A-375. The liposomes formulated with lunasin achieved 82.14 ± 3.34% lunasin encapsulation efficiency and improved efficacy by decreasing lunasin IC50 by 31.81% in B16-F10 and by 41.89% in A-375 compared with unencapsulated lunasin.